The manifolds between the 5.3 and 6.2 are different. Pretty sure it won't bolt up, 5.3 has 2.75" tubing behind y-pipe, 6.2 has 3.5".
Just have a shop weld in a flo-pro big oval muffler that is slightly louder than "stock sound"muffler. PN 2510 is a 3.5" in and out, used on NNBS 6.0 and 6.2 trucks. A muffler shop should be able to make adaptors to go from 2.75" to 3.5", plus it will be TONS cheaper than what sounds like you are working on