As a Shen main in Season 4 and now season 5(He's one of my most played anyways). I've had very little trouble with the champs you mentioned.
Edit - Honestly as far as lane matchups in general go, I've never had an issue with most of the AD top champs and bruisers, being able to build armor straight up against them allows you to tank minions early enough that fighting in the minions with his sustain makes them almost a non threat after a couple levels of Q.
Nasus - Because of Shen's Q sustain and if you go feint at level 2. Shen EASILY out trades an early Nasus. and after level 4(or 2 if your jungle wants to super early gank). I have never had a problem against Nasus and have usually forced him out of lane multiple times before a tower goes down.
Jax - Bit rougher early game, but once again, haven't had many problems against him early due to Shen's sustain and ability to poke while farming.
Vlad - Honestly, this one I've had go both ways. During the early laning phase, Shen should be able to dominate Vlad just based on cooldowns and abusing his passive, Q and taunt. After 7 it becomes much more difficult due to Vlad's Q CD getting low enough to actually sustain during and after trades.
Rumble - Sadly, I do agree with you on this one. a decent rumble should be able to wreck Shen early and throughout laning( Ironically against Rumble I usually have a creep lead because of how hard they push and the nature of Shen's single target farming). However I have had games where, as Shen, I got an early Spectre's Cowl, and usually was able to stand toe to toe with him much more. The later lane matchup on this I think comes down to player skill and awareness of Rumble using his ult and getting out of it rather than fighting in it.( In lane getting out of the ult during a melee fight with rumble should be as simple as stepping to the side).
As for other AP top laners, If you can finish an early Spirit Visage, your sustain with Shen should usually outpace the damage they can put out. However that does make him much weaker against any adc's or AD champs the enemy team has.
As for playing Shen top vs Mao or Gnar. I will take Shen top over those two any day of the week. Mao and Gnar are both great, don't get me wrong, but the reason you play Shen, is because of his global map presence(The only truly global ability left I believe that isn't a skillshot ala Ez/Ashe/Jinx). Which if done properly can turn fights and losing games around. I've managed to save many and adc/support even when I get stunned while ulting just because of that shield I gave them. Or turn around a losing bot lane because the enemy chooses to dive the turret and I manage to ult in and then taunt the enemy under turret. I've also managed to get double and triple kills while surviving dives on the top turret.
All in all I think Shen is a great champ to play and master, but I will admit that in solo queue, he is under appreciated because people don't always know how to work with him.(Tanky support or jungle who runs away from a fight as I'm ulting in making it hard for me to get a good taunt in).
Now I will admit this is from the view of a consistent Gold player(Managed to achieve Gold 1 in season 4, just got back into gold from Silver 1 during the soft reset) and Plat and up players likely have a much greater skill in managing a Shen, but I still believe he is a solid pick for a team.
Alright there's my 2c, I fully expect every point to be torn apart, I just hope its for actual reasons not the normal, well you are gold/silver so you suck anyways crap.