Umm. I think you should have bought a Gen IV core to keep everything more simple.
The major difference between the Gen III and IV on the block are:
1.) 24X vs 58X crankshaft reluctor wheel. The wheels themselves can be swapped from one to the other, however. But needs to taken to a machine shop unless you want buy the Goodson tool. Obviously, crankshaft is coming out for this.
2.) Camshaft position sensor and count. Gen III has the cam sensor on the rear/top of the engine and it's a 1X reluctor. Gen IV has the cam sensor on the cam sprocket and is a 4X reluctor. An LS2 cover will get you the provisions for front cam sensor and there's a conversion harness that goes from a Gen IV to Gen III... I'm not sure if there's anything the other way around, but I'm sure you can do it.
3.) Knock sensors are on the top inside the valley cover on Gen III vs down on each bank on Gen IV. Going from Gen IV to Gen III, there's a harness to convert the different location and the smaller threaded holes can be reamed and retapped for the larger thread of the Gen III knock sensors... I'm not sure what going the other route would entail.
4.) I'm sure there's other smaller stuff to consider...
So to summarize, I'm sure it is possible, but you can see there's plenty involved. I'm assuming no DoD/AFM stuff would get reused, of course.