Lol, I'm am an avid Roadkill fan!I wouldn't waste too much time with diagnosis. Even if you get it running, it's a total crap shoot on the longevity side of the equation, unless you pull it apart for inspection, rings, and bearings. Why waste the money on a 305?
Cheapest, easiest is to grab a running 350, then stab it in.
As far as the cheap <chuckle> LS swap, I thought the same thing when I did my Series 2 swap. For all intent and purpose, it is an LS swap minus 2 cylinders. Almost all of the wiring was the same, and the Series 2 block has all the LS goodies like a roller cam, EFI, cross bolted mains, etc.- just add a counter balance shaft in the cam valley. I think it still cost around $2k, even getting everything (motor, trans, wiring, computer) for some Olds parts in trade. That was 3rd venture into the modern engine retro fit, but I used all factory parts. It also only lasted a couple hundred miles before spinning the #3 rod bearing (90k hard, neglected miles at install).
You need to watch more Roadkill. "Don't get it right; just get it running" - D. Frieburger
That said this needs to be nice driver, not a Roadkill car.
I actually have a good running tbi 305 in my wagon that I think I'm going to put in. I would like to keep the tbi system as well if I can.