$800 is way too much IMO for a 5.3 missing things. I can get complete turnkey 5.3's with all accessories, harness, PCM, sensors, MAF, etc for less than $600. Even with freight, its a better way to go.
The drive by wire or DBW is super easy to deal with. Too many folks raise a stink because they are scared of it or something. Keep the factory EFI. You won't save a dime going with a carb after buying a carb and the correct intake manifold and ignition box.
The T-56 is also a great trans for your goals. Yes, a World-Class T-5 will also work, but its a much weaker trans and really wouldnt save alot of coin.