'69 Barracuda T56 swap, floor, cross member

Is there any room to shift the engine forward? Like even a tiny bit? Basically not modifying mounts or anything, just loosening the engine mounts and seeing if it will shift forward on the mounts.
I put the cherry picker on the engine lift plate, loosened both motor mounts, and moved engine forward as much as I could. I would have to move engine forward 1/4 inch or more to alleviate the clearance issue at floor/heat duct and giant dents in headers would be required. I could widen k frame motor mount slots to allow engine to go more forward but then headers would need big dents to clear steering linkage.

I am going to measure driveline angle and pinion angle before I do anything else.

I wanted to get AC hooked back up for next summer. I removed AC from car back in 1981 due to blown head gasket and never got around to putting it back in car. So really the whole HVAC box needs to be taken out anyway but was hoping do that after trans swap. But leaning toward taking hvac box out now, finish trans swap with hvac box out, then look into modifying floor ducts while hvac box out of the car later one.

But I think its best to measure driveline and axle angles like you suggested verify those are within specs before doing anything else.