There's definitely no damage cap per shot that you're currently hitting. I'm not sure there's a damage cap at all on any mob, in fact. There was in 11... It was obvious there. You could go hit a level 1 bunny at level 75 and you'd hit it for the same damage you'd hit a level 20 mob for because of fSTR, attack caps, etc.... But on FFXIV if you go shoot a R1 Marmot, you'll do like 3k+ damage. If you hit a r30, it will do around 1k... And continue to drop the higher the rank of the mob, meaning the cap is either nonexistent, or well above 3,000.

(We know the damage cap is 9,999 currently, from raged NM's)

Now, you're surely going to say "but it's an NM! It's not a marmot!" And that really doesn't matter. If it did, then you wouldn't hit the faction buffalo for more than you hit the Great Buffalo for, because they're both NM's. There is no cap, it's just that NM's have much higher stats than normal mobs, so their vit and def compared to your str and atk are much, much greater. It'd take a huge stat increase to go up slightly in damage because the gap is so large.