I agree that Pantheon is currently outdated, and although some Solo Q players maybe content with the way he is now, we almost never see Pantheon in professional play due to many flaws:
Global presence from Grand Skyfall and rest of kit outclassed by more common professional picks like:
Shen: Doesn't use mana. Has a more useful global ultimate, and AoE taunt (harder hard CC). Spirit Refuge has an Area Effect and more reliable against AD carry damage burst than Pantheon's Passive.
GP: Global Ult with Aoe Dmg/Slow that lasts way longer and doesn't need a channel. Doesn't endanger GP's position because he doesn't move like Pantheon does with Grand Skyfall. Scales way better into late game with massive AoE teamfight dmg and Parrrley poke that can Crit more reliably than Panth's E Passive.
TF: Ult is Global and grants True Vision, plus Gold Card Stun is more immediate and doesn't require going into melee range where they can be focused/peeled off more easily. Plus other ranged > melee benefits.
Other Top Lane champions
like Rumble, Gnar have good enough lane poke, and can lockdown ENTIRE TEAMS rather than just one enemy.
like Mao'Kai, Nautilus can get tanky enough to ignore Spear Poke, and easily lockdown Pantheon for ganks/tower dives since he has no escape methods. They are also better escapists themselves.
like Darius, Fiora, Renekton, Kled, Jax, Riven, Camille are more mobile, and scale better/become better duelists when they get more items (professionals tend to get those items faster cause of better CS) and better sustain (which Pantheon doesn't have). They will last longer in fights and deal way more damage, consistently.
Pantheon has terrible wave clear, runs out of mana quickly, very vulnerable to high dmg/high CC AoE abilities. He also scales poorly into the late game.
355 base movement speed is still not enough to make Pantheon a really good roamer/chaser.
Right now Pantheon is not a bad champion though. He is very good in Solo Q (54% top win rate in Korea) where solo kills are more common, teamfights (including the "peeling for carries" aspect) are less coordinated, and enemies have less respect for your Grand Skyfall capabilities. Still besides his ultimate, Pantheon's kit is very one-dimensional compared to many of the new champions Riot releases, and I think Riot can do him more justice like they did with Ryze, Yorick, Warwick, Galio, and Urgot.
I think your rework idea is significant because it fits the Greek warrior theme that Pantheon embodies better than any other idea I've thought of or seen. I can also see the "niche" that you gave him; the closest champion I can think of to your proposed kit/playstyle is Wukong.
Wukong with Stone Skin passive can gain up to 20/30/40 armor AND magic resist, not based on combat but the amount of visible enemy champions within 1400 range radius of him.
Like Wukong's Stone Skin, Hold the Line should also provide Magic Resist per second. Hold the Line would be a great passive for extended fights, something Pantheon currently isn't really good at. The part where you said that Spear Throw doesn't count as entering combat is unnecessary. Pantheon's current Spear Shot has a range of 600, and you reworked it to be even longer. Hold the Line requires Pantheon to be 300 range from enemy champions while in combat. If Pantheon uses Spear Shot at a range of 300 or shorter, it should proc Hold the Line/enter combat.
Currently, the scaling for Pantheon's Spear Shot is 65/105/145/185/225 (+140% bonus Attack Damage). Bonus attack damage means the attack damage gained from Runes/Masteries/Items/Buffs.
Your reworked scaling is 50/100/150/200/250 (+100% bonus AD). You made it scale a bit better, but lowered the based dmg for levels 1-6 which is where Pantheon's poke is supposed to be the most effective, as well as lowering the scaling of bonus AD by 40%, which is A LOT. You didn't include a Cooldown, so I assume it's unchanged: flat 4 seconds.
Since the reworked Pantheon's Q is longer range and has a slow effect for enemies moving toward you, perhaps lowering the damage is justified.
Pantheon has the highest base movement speed (tied with Master Yi) of 355. He also has a pretty decent melee auto attack range of 150. Since his Q can now slow movement toward him, keep in mind that he now has the potential to kite back on enemy melee champions with shorter or similar auto attack range, which is really good for a duelist when trying to turn a fight around.
I like the idea of (W) Defensive Stance replacing Aegis of Zeonia and Protection passive. Reworked ability is even more useful in that it provides a full-on spell shield.
You need to elaborate more on this new ability though.
The logic behind this ability is also very weird. I mean, if you block a Nidalee Spear after charging your shield enough, Nidalee still gets damaged/stunned even if the spear comes from 1500 range (max range) away? Must be some kind of enchanted shield.
The way I see it, Defensive Stance would be similar to Rammus' Defensive Ball Curl, since it has the self-slow effect which can be cancelled upon reactivation. 50% self slow is a lot though. Rammus' self slow is 30% (It used to be 60% and even Riot agreed it was too frustrating), but since Defensive Ball Curl is not a one-time spell shield effect, I'll leave the self slow of Defensive Stance up to your interpretation, but at least allow the ability to cancel Defensive Stance (thus cancelling the self-slow).
If I could improve this new ability, I'd say make it an AoE effect (like a Shen Spirit Refuge only it stays around Pantheon as he moves), which can pass the effect onto nearby teammates (Mage mains cry).
(E) Go for the Vitals needs a specified range. Talon's Noxian Diplomacy bonus effect procs at 170 range. Jax's Empower autoattack has a 50 range increase, or 175 range. Wukong's Nimbus Strike has 300 range (125 range increase). These are just some references.
Heartseeker Strike had a 10/9/8/7/6 second cooldown.
Either base damages could scale a bit higher (190 at max ranked is very low, even lower than Spear Shot, and the 70% scaling of bonus AD is half of Spear Shot's scaling). Another reason why the base damages could be higher is that the initial passive of Heartseeker Strike allowed Pantheon's autoattacks to crit (deal x2 damage) champions below 15% health (Spear Shot still dealt x1.5 damage). The reworked 20% health threshold shouldn't make too big of a difference, but you reworked it to deal x1.5 damage instead of double. The x1.5 damage increase is fine though, since it procs on any champion that is stunned.
It should also work on champions that are feared, knocked up, taunted, suppressed; any form of hard CC.
Phalanx ultimate sounds really awesome. The picture of Rakkor/Spartan warriors dropping down from the sky beside Pantheon is fantastic. Historically, Hoplite phalanxes had about 8 men or more. But Pantheon's case he could have 6 warriors, 3 on each side of him at each 100 range interval. It seems like the ability would work like a moving wall (moving at 50% of Pantheon's movement speed) that deals damage in a way similar to how Azir's Emperor's Divide knocks enemies back. The angle of the phalanx wall should remain as it was cast, so Pantheon players would need to learn how to angle it correctly.
Another thing you should add is that the self-slows of Defensive Stance and Phalanx do not stack.
One problem with the ability that needs to be addressed is how will the ult would function in tighter spaces that can't encompass a 600 range long wall?
Another problem is that since this phalanx wall can move, and enemy champions can't move past it, will the soldiers also knock back enemy champions that stand in their path?
Would the attack speed of the soldiers would be the same as Pantheon's attack speed?
+75% bonus AD is quite low. Perhaps it should scale with base AD instead, or the scaling should be raised to a higher percentage.
The duration of the ability needs to be specified. Rumble's Equalizer has a full duration of 6 seconds. Alistar's Unbreakable Will is 7 seconds. Fiora's Grand Challenge, Jax's Grandmaster's Might, and Gangplank's Cannon Barrage are 8 seconds. I think the duration of Phalanx should be like these abilities.
The cooldown for Fiora's Grand Challenge is 110/90/70 seconds. Alistar's Unbreakable Will is 120/100/80 seconds. Jax's Grandmaster's Might is 80 seconds. Phalanx cooldown should be similar to these abilities.
Currently, according to op.gg, Pantheon's Core Items for Top Lane are 
Ghostblade and 
Cleaver. Other common items are 
Duskblade, 
Maw, and 
Deadman's.
With this reworked Pantheon, Ghostblade will still be useful on him, perhaps even more useful than before since Ghostblade Active will relief Pantheon a bit from his self-slows on Defensive Stance and Phalanx.
And if Defensive Stance is AoE like I proposed, He will also be quicker to help protect his teammates with the movement speed.
So Ghostblade will probably remain a core item on Pantheon.
Black Cleaver will also retain much of its usefulness: the flat movement speed from Phage should also relief Pantheon of self slows and help him kite even better with Spear Shot when dueling.
Unfortunately, reworked Pantheon can no longer get up to 3 stacks of Cleaver armor reduction with Heartseeker Strike. However a charged Defensive Stance now deals physical damage (unlike Aegis of Zeonia magic damage), so it can give one stack of Cleaver unlike before.
Phalanx would be a really compatible with Cleaver, since Pantheon's warriors can repeatedly stack Cleaver on nearby enemies.
Death's Dance (and Maw of Malmortius passive) would also work great with Phalanx, giving Pantheon a lot of sustain and tankiness. Add a Ravenous Hydra for even more sustain and the AoE/extra Black Cleaver proc, as well as waveclear that Pantheon needs even more now that he no longer has Heartseeker Strike.
If Phalanx soldiers could also proc on-hit effects, then Frozen Mallet would be a great buy, granting a good slow to nearby enemies.
Hope this helps.
