[AcampoDave]

That may have something to do with that flapper gizmo on the exhaust being messed up. It could be a poorly functioning choke, a carb needing a rebuild, maybe a vacum leak, and yes, in part perhaps a worn out distributor.
But remember that it is fairly normal for a carburated engine to need a warm up period in cold weather. Especially when the carb is hanging off the side of the motor. Dropping another thousand bucks on it, as you said, may only wind up in disappointment and I've seen it many times when big ideas don't pay off and another basket case project gets sold on Craigslist. (Been there, done that)

Starting with the basics, a good tune, a distributor and ignition system that is verified to be fully functional and making sure your stock carb and its related components are up to snuff would go a long way toward buying the time to research any future engine mods more thoroughly