I just went out and looked at our JK. It's damn near perfectly similar. I installed this myself and I am 100% sure that I did not put the winch through the bullbar. I put it in between the grill and the bar, and I remember the grill bending because it was tight as fuck. We also have the 10s on this Jeep.
View attachment 6642
View attachment 6643
If you're worried about damaging the grill, loosen the bumper bolts a little just to move it forward a little. But I see no way that you're going to fit that winch through the front opening. I think it has to go in by the grill.