A 32 GTR rotor is 32mm; min thickness would be around 30mm.
Rotor width won't stop the calipers from working, there is more variation in piston extension with worn pads (6mm approx) as compared with new pads.
The pistons simply push out further to make contact with the rotor. You can run the pads down to the backing plates, on a min thickness rotor; and still keep the pistons captive.
Good suggestions from 3Katz, and normally they are quite easy to bleed.
Did you push the pistons all the way back into the caliper to remove as much air/fluid from the calipers before starting?
Obviously the bleed nipples are at the top on both sides?
Silly question, but I've seen people fit Sumitomo's upside down, then go mad trying to bleed a caliper that will always be full of air.
Once 1 piston pops out, compressed air won't work. I found it was necessary to lever the pistons out gently with a pair of levers in the dust boot groove.
If you protect the caliper and pistons well, and the shafts of whatever levers you use; there is nothing wrong with doing this.