I’ve got a gen 4 g22, and it seems like 4th gen guns are known for having a heavier trigger. However this issue seems to stem from a Lone Wolf conversion barrel.

After shooting about 100 rounds, the trigger begins to get extremely stiff...like NY trigger heavy. It won’t be like that for the first magazine or so, but after a couple mags it starts to stiffen up something fierce. It doesn’t do this when shooting .40, only with the conversion barrel in it. The barrel has been flawless, no problems except for the trigger issue.

Any idea what could be causing this?

Just my opinion but I don't know how there could be any way the barrel could effect the trigger at all.
Are you using 9mm magazines with 9mm rounds? The magazine sits right next to the trigger bar so once
the trigger starts getting stiff take off the slide and look at the trigger bar and check trigger function while magazine
is in (make sure magazine is out and gun unloaded before removing slide). Then reinsert magazine and check trigger function.
maybe magazine is putting pressure on trigger bar or getting in the way of full pull?

Oil the contact area between the connector and the trigger bar.

If this area ever gets bone dry, the metal will gall and the trigger can bind up.

It needs only a microscopic amount of oil to prevent this.

Sounds like that's what your guns doing