Dead Men's is pretty good on Garen as a 2nd or 3rd item. I only rush it in a few matchups, though, such as against Gnar. I used to rush it a lot but I don't feel like the meta really favors this right now.
Dead Men's has a couple of problems. It's biggest problem is lack of waveclear. If you get Dead Men's for the movespeed, often you'll get to fights later than you would with Sunfire, because it takes too long to get the wave where you want it.
I've also noticed that with CoC and Warlord's Bloodlust becoming popular, BC + Sterak's isn't enough damage to do your job. Sunfire seems to get you just that last tiny bit more damage that you need.
If you've already got BC, Sterak's, and Ghostblade, though, you've got plenty of damage to 100-0 squishies.
As for Split Push Garen, I used to PD and Triforce. I did this quite a bit when the Rylai's meta was in full swing. The whole point of this build is to be so fast that you are able to run people down even while you're permaslowed. With the Rylai's nerf this build is less necessary.
BC, Executioner's, and PD will let you split vs Nasus. BC and DD will let you duel thornmail tanks like Rammus or Malphite.
PD and Triforce both have decent synergy with Garen's kit because he has so much base AD.
Most of the time, recently, though, I've been just building Sunfire to split. Sunfire lets you get the wave where you need it so you can rotate to join your team. Garen is pretty average at taking towers, so it's usually better for him to join his team ASAP.
A good Sunfire Split build could also include Dead Men's. Rushing Sunfire and Dead Men's makes you insanely tanky in the mid game, while being able to quickly push the wave and rotate.
My old core build was Dead Men's + Sunfire into BC then Sterak's. This build leaves you with very low damage against non-villains until you get Cleaver, however.
The game seems to be having quite a bit of damage creep recently, though, so I often find it necessary to get Randuin's in order to survive in the middle of a teamfight, where in previous seasons Sunfire and Dead Men's was enough. A lot of games I'll get all 3.
Hope this helps!