the biggest issue of doing the LS/LS swap is, while they are all the same on the outside, internally, reluctor wheels tend to be the bane of swappers existence. GM changed the number of notches on the reluctor wheels in and around 2005 - but they didn't make a wholesale change, so two motors, of similar vintage could have different reluctor wheels. If they are different, at minimum you have to change the computer - but since about everything is interrelated from the computer, that change could make for numerous other changes down the line. I'm considering swapping my 5.3 for a 6.0 or 6.2 motor, but the first step of that question is computer interchangeability. The computer that's in the Alpha can easily handle more cubes, but again, the reluctor wheel issue is a big one (or not at all if you know that's an issue and mitigate it)
frankly, what I'd like to find is a 6.0 from a similar vintage H2 along with the 4L65e transmission. again, they bolt up, but there's more power and more beef in the transmission.