After experimenting with many builds, I finally have it. Team fight Tryndamere:

The team fight oriented aspect of this build relies on the fact that Tryndamere has the most health at level 1 scaling to the second most at level 18, and the fact that people always focus Tryndamere first if he is within range in a team fight. We will leverage that to become a mundo-level damage sponge.

Basically we are going to abuse the hell out of it with gargoyle stoneplate.

You CANNOT afford to get any sort of real durability within your first 2 items as Tryndamere (except frozen mallet under certain circumstances). So the first two items are very normal: we want to maximize our damage with these two items because our other items will be mostly dedicated to shoring up our ability to team fight.

Thus our first two bit damage ticket items are:

You could replace phantom dancer with statikk shiv but this build lacks the attack speed to stack shiv quickly, and the fact that you are able to stay alive much longer than normal even while surrounded means the value of phantom dancer's bonus movement speed increases dramatically.

Your boots should almost always be

After that we need to really start buying utility and durability for team fights. Typically your next item will be:

Up until now we haven't bought anything too crazy. These aren't the usual items for Trynd, but they aren't unheard of. The next two items is what allows you to actually participate in those mid and late game team fights:

Generally the moment you get within range of any real damage in a team fight as Tryndamere you will always be bursted and forced to ult. The idea behind this build is, what if you can keep yourself high enough on health so that you don't need to ult? The pressure of Tryndamere still being alive and not having to die or retreat within 5 seconds is immense, and it forces people to use even more burst on you.

Your goal as Tryndamere then is to absorb literally all nukes and ults on the enemy team. The first barrage will be negated by Gargoyle Stoneplate (Tryndamere will have over 8 thousand health in that form). Although you don't necessarily do a lot of damage while in Gargoyle, you effectively force the enemy team to throw damage away on you as Tryndamere, and the real utility of Gargoyle here is that you can make those nukes mean nothing. You will just do piddles for damage for 4 seconds-- woopity doo, it will take around that long to get to your targets while being knocked around with cc anyway!

Once the enemy team sees that you are still alive and you haven't used ult and you are making your way towards the backline, they will toss out their more expensive spells, perhaps even a few ults. The enemy marksmen will start to focus you exclusively. This is where Gage activates, wasting more of their time and damage.

Even after all that, with the enemy team throwing damage at you for a solid 4 or 5 seconds, you still have your health bar AND your ult, and the enemy team is basically out of spells. That allows you to actually do some damage during your ult.