Rear end is definitely tweaked upwards then.
This, sort of. There's something radically wrong that shouldn't be that hard to spot.
For instance... why is the drive shaft even rubbing in the first place? My driveshaft isn't that close to rubbing anything.
There aren't that many attach points for the diff and subframe. Get a bright light and go look.
For a far too bizarre theory how about this: When you accelerate, force is applied via the bottom of the rear tires. The reaction to that force rotates the front of the differential upwards and the driveshaft makes contact.
Let it sit for a while and the caster slowly lets whatever is broken lower the front of the diff.
Just for grins, measure the distance from the front of a tire to the fender, go for a rip, measure the distance again. Let it sit and measure again.