from the searching i've done, it'll end up being a custom flywheel from advance adapters. it has to be thicker than a stock flywheel.
and yeah it'll bolt up, it only uses 5/6 bellhousing bolts though.(not a problem)
there is some info you can find by searching on this site. you should know that custom mounts will be needed in addition to a custom wiring harness.
edit: the shifting problems you're experiencing are more of a tuning issue. the 5.3 has more torque than a tbi 350 ever came with. it's often they dont feel like it because from the factory these newer trucks are programmed with something called "torque management" to limit the load on the piece of junk half ton auto tranny gm still put in these trucks.