Pathfinder 2e Character Discussion

Honestly, Monk + Wrestler or Monk + Barbarian (giant) would probably make a better grappler overall, and do more damage over time, since the Monk inherently does more damage from unarmed attacks. I know what you mean about the fighter doing better damage, but that's sort of predicated on playing a fighter as a plain vanilla fighter. Once you've sort of focused on grappler, you're chucking part of the fighter's advantages out the window.

If you do want to stay with fighter as your main class, my opinion is that wrestler is clearly the better choice, mostly because it's entirely focused on grappling. Take farmhand background, snagging strike as 1st level class feat, wrestler dedication at 2nd which gives you titan wrestler, then combat grab at 4th. If you make it all the way to 8th, that's when the really fun feats come online, like whirling throw.