After some more phoning and mailing back and forth, I parted with the money for a new LS2 crate engine. Now the waiting game begins. Hopefully sometime soon I should be able to collect it.
In the end I went for the complete engine package instead of building from bare or short-block. The deals you can get on crate engines these days are so good that building one from scratch is, at least money-wise, absolutely not interesting. I would have liked building one though. Oh well, it's not as if there are no other jobs to complete.
There is no way this engine goes into the cold and damp garage for now, so the view from behind my desk should considerably improve when the engine arrives. :D