Welcome to the Team Fonzo!
A MUCH better idea is to go the bone yard a grab a 350 out of a pick-up truck and rebuild that to your hearts content. There is only one numbers matching block with all of the date codes cast into it. I recommend pulling it, draining fluids, covering all holes, and then bagging it to keep moisture out of the engine. You can store it in the garage or up in your attic over the garage, but you want to store it. That is if you are really worried about numbers matching.
You can build a Dart Little M block that has perimeter aftermarket heads a newer high rise manifold that flows half again better than anything Chevy ever cast and a small cap HEI with a digital ignition box inside your glove box. A Hydraulic roller cam (I prefer a solid roller myself but I don't mind the maintenance required) and even a set of two and a half inch Rams Horn cast iron manifolds and of course two cans of Chevy Orange paint and it can be made to look just like your factory motor; only pumping out a hundred to a hundred and fifty more horsepower.
If you scatter the guts out of a junk yard block you won't feel nearly as bad as you would if it was your "born with" being scraped off the track. If you go the Dart block route you can build a much bigger displacement small block than the 350 for about the same money.
Big Dave