^^^ what he said
The dbw will save you some time, and simplify things. A T56 is a great conversion, but I am not sure a 5.3/T56 could be done for $2000 unless you find a really great deal on the transmission with a good clutch.
GM mated a 5 speed to some of the 4.8L that might be an option. I don't however think they would withstand a lot of power, but for what you describe that may be an option as well.
'92 Fullsize, swb rc
5.3L/T56 conversion, comp XR275 HR cam .566/.568 lift 222/224 duration 112 lsa, crane dual springs, trick flow push rods, K&N Filter, Nelson Performance tune, Keisler shifter relocation kit, Boyd Coddington Smoothie II 18x8 235/55 up front, 18x10 295/45 out back, 2/4 drop, eaton lsd w/4.56 gears