I was 2-3 levels ahead of their highest level at the teamfight
This sounds like a potential issue with how you're using your momentum.
Fighters, generally speaking, are amazing duelists and awful team fighters. A fighter will usually convincingly beat any other archetype (tank, assassin, marksman, mage, support) in a straight-up 1v1. As a counter-balance to that, most fighters are among the worst team-fighters in the game, lacking the same presence as most marksman and assassins - and especially tanks, mages, and supports.
This is basically why a large number of top-lane champions are solid split-pushers. Forces 1v1 situations to happen.
Another thing: ~half of the fighters that are fighter/tanks (rather than fighter/assassins) tend to almost always be Mid game champions, hitting their major power spike and carry capacity during mid game. Nasus is really the only fighter/tank that's truly a late-game champion, otherwise you're looking at a slew of bruisers that want to steamroll the enemy team into submission at the ~25 minute mark and close out the game before 30 minutes.
Bruisers like Volibear that get a lead are also completely terrifying. They have no bothers to give about towers and will dive you 5 minutes before towers usually cease being safe-zones.
When ahead, you're also a massive catch-22 to deal with. Most high-damage/squish champions can be delt with via forcing team-fight situations and just focusing them with everything. Bruisers? When you're ahead you're as effective at sponging damage as an actual tank, and often as damaging (if not more so) than major threats like assassins, mages, and marksman. You're in bad shape if you focus them, you're in bad shape if you don't.
You've got a lot of wieght to through around is what I'm getting at, and you want to be a wrecking ball when that happens.
Also:
The reason champions like Irelia, Jax, and especially Tryndamere work so well with 10 kills is because those are specifically late game champions (ie scales well with gold, pretty useless without gold).
Tryndamere in particular is in the running for the worst champion without items.
Their end-game for winning the game really is turtling to 40 minutes in, getting full-build, then overpowering their opponents. That's the in for blowing up the Nexus, that's the contribution. Jax and Irelia probably more ~30 minutes.
You're end-game with a champion like Darius is getting a lead early, then pushing that advantage for every ounce of power it's worth ~20 minutes in and overpowering your opponents.