I run 275/60/15's on a 70 Cuda with Torque Thrust wheels but I chose either 4.75 or 5" back space. Don't remember which. No contact.
I am thinking you must a good 1" tween tire and leaf-spring? I have about 3/4"

Edit after reading your post above. Yes the close spring contact area is the rear segments, I thought about intalling the rear offset hangers to gain clearance, but didn't have to for 275/60/15s. In fact, I think it may be possible to fit 295/50/15's with the offset hangers.

So now you are sitting on a set of barely used 4.5" BS TT's?