I'm not sure trying to out-heal the sentry is a good idea. Wouldn't it make more sense to bring a Scout with Bonk to distract it? Once Valve makes the thing headshot again, you might as well forget about putting a Heavy in front of it. Even with 3 Medics attached, the thing will just plow through the Heavy, not to mention that the Engineers will just out-heal the damage the Heavy does. No no no, just distract it with Bonk and have a Demoman lob some grenades to clear the summons and a DH-wielding Soldier to actually kill the thing.
Since you won't be bringing a Pyro, keep an eye out for the Spies that get summoned when you capture the first control point. Sometimes they literally appear behind you right after you get the point, sometimes they only show up while you're fighting the sentry. One of them is a Boss-Spy, he's the one with the Level 39 Noble Amassment of Hats and the Level 53 Dead Ringer. Luckily, he's using a laughably weak pair of a Level 21 Revolver and a Level 23 Knife, but that doesn't make him easy! It's very hard to keep him dead and he WILL backstab you if he gets the chance. It might be a good idea to farm him for awhile to get his mid-level Dead Ringer, they go for about 1 Refined, 2 Reclaimed on the open market. Don't bother trying to get his Amassment, there are easier places to get higher level Noble Amassments. If you get his Level 12 Camera Beard, nobody will pay you for that garbage. Just trade it with the NPC's to remake one of your other hats.