I don't believe that the transmission tunnel is bolted in, in your '83. I believe that GM stopped that with the body change in '81. My '90 Jimmy had it spot welded in with seam sealer.
I use 18" or so of extension with a swivel impact socket. I even have a 36" extension that can come in handy.
When my Dad swapped the engine in his '90 Blazer, we pulled the front clip after the hood was off. You have to wiggle things just right, and we pulled the front tires and set it low on jack stands so that he really had room. It was easier to work in the engine swap, but added a fair amount of time. We also propped the radiator up to start the engine before we put the front end back on. That way we could still get to it easily for any issues.