If the heads are 243's and are stock on a 6.0L engine, you are looking at an LS2. The 243's also came on LS6 engines, but are 5.7L engines.
If you are actually wondering which engine came out of the Avalanche and it has 243 heads, you are looking at a 5.3L with some other than stock heads. They didn't install the 243 heads on the truck engines.
You should be able to source any truck wiring harness and it will mate up. If you are going to put a car accessory bracket up front, I suggest you get a wiring harness for an LS car (97-02 Camaro/Firebird). I don't think I'd try a GTO wiring harness, but it could work.
As for the 94 T-56, it will not work behind the LS motor. There are a bunch of differences besides just the bell housing. The clutch release (throw out bearing) is completely different (push instead of pull). I believe the input shaft is different as well. You need to find a T-56 out of an LS car (Camaro or GTO) for it to mate correctly.