Engine requires 20 degrees of initial to idle well...

Something's definitely not right there. My car is set up at like 18* advanced, but it does ok there set up at 36* all in. You've got something else going on.

Did you check TDC? I mean, not just check that the dots line up, but actually that #1 is at true TDC when the marks are lined up?

Was the cam degreed at all?

What's the deal with your carburator? Has it been used before, did the engine run well with it as is? Or is it new?

What has been changed recently? I'm assuming the cam is new, what else?

I would start by finding true TDC and making sure everything lines up accordingly. A fair number of new dampers are marked incorrectly or inaccurately, and timing gears and chains aren't much better. Ideally you'd check it with a piston stop, but even if you just look down the #1 spark plug hole with a flashlight while a buddy turns the engine by hand you can get fairly close, just have them slowly advance the engine until the piston "hangs" for a second. I usually go past it and then back a few times to make sure I'm in the right spot. Not perfect, I set mine up with a dial indicator when the heads are off, but it sounds like it'll be more accurate than what you've got already...