Joined: Nov 2016
Welcome to AFM, Dvelek! It sounds like you've got a few issues going on. It's going to be kind of hard to guess which issues you might have, but I'll try and list some likely ones for you, so you can hopefully figure it out yourself.
Let's start with low compression, and the head rebuild. When you had them done, were the valve seats bad? Normally, compression issues are due to poor ring seal. Only if your exhaust valves are really bad will it usually leak enough to cause compression issues. So how did all that go down? Did you do another compression check when you got the redone heads on? What did the rebuilder do to the heads to fix them?
Which brings us to the second thing: smoking. When does it smoke the most? Just when you start it? The whole time it's running? Is it producing oil smoke (puffs of white/grey/blue-ish and smells a little like bacon to me) or is it black smoke that smells like fuel? If your valve seals are shot (maybe the person who fixed your heads failed you here?) they will let oil drip into the heads, so when you start your engine it smokes a lot at first. It will also usually blow a bunch of smoke when you let off after accelerating. However, bad ring seal will also suck oil into the cylinders, so that will smoke on decel pretty good too, sometimes. If your rings are not sealing, you will notice a lot of blow-by coming out of the oil breathers. If you have a PCV hose and it's properly hooked up, you might take it loose from the carb base or manifold, plug the nipple for it, and run the engine to see if a bunch of smoke is coming out of there. A *little* smoke is normal. Steady puffs of it might indicate worn rings, in conjunction with a failed compression test.
What kind of ignition system does your car have? Is it points? Those do require maintenance, even though they work very well. How's your car run?
I know it's a lot of questions, but having the answers will probably help figure out what's going on.
I smile a lot. It makes people wonder what I'm up to...