1977 Pontiac Firebird Back fire not running

Hi, the car is actually a 1949 Chevy deluxe with a 1977 pontiac firebird/trans am 400 CID in it. Here's the problem I'm having. The engine has a healthy hiccup and backfire. It's even caught fire a couple of times! To explain in detail.

I purchased the car thinking that the car needed a tune up or the carburetor was shot. When the seller showed me the car he had to pump the hell out of the gas to get it to start. Then for the first few miles had to two foot it to keep it running! Now I just assumed old carb along with no choke, car is cold therefore that explains the two feet driving! Well little did I know even when the car is hot the first few miles you have to two foot it. While sitting at idle at a stop light in gear the engine would also randomly make a hiccup feeling, kinda like when you have a bad motor mount that slam you would feel throughout the car. It would make that feeling every time sitting in drive, Never at the same time as if the cam was worn but just very spur attic. Also the car had A heavy vibration.

What I've done explained in detail
I went with my gut, purchased a new edelbrock 650cfm, changed the plugs wires, pulled carb off seen that it was a single plane manifold so I changed that to a dual plane manifold. I installed the new carb, set the timing (distributor is an hei) which was advanced to 30+ before tdc. Along with the plugs being gapped out close to 100. And at this point the car became even harder to start, ran a lot worse and the car was set to factory specs. The internals are stock for this engine. I finally felt that I got it running decent enough to take it for a ride
As luck would have it I backed it out of my driveway and the car just died? No backfire, no sputter nothing. It
Was like I turn the key off. Well the car was on fire! Carb was burning and ended up burning my hood.

I returned the new edelbrock with hopes that it was the problem and went with a Holley 600 cfm. I installed that, had to reset timing again? Got her to fire up rather easily. I thought this solved the problem but it didn't ! I took the car around the block, same problems as before just a lot worse along with backfiring. Got her home, was messing around with it and realized that if I hold the throttle underneath the hood at a steady 1200 rpm the engine began to bog down really bad and moments later backfired slightly and I had another fire to put out! In order for me to get the car started again I had to move the timing around to get it to fire after, it was already set! I also noticed will setting the timing there doesn't seem to be much of a diffence in running style when I remove the vacuum advance line. Btw I did properly adjust the carb.

My thoughts
I've been building and working on these old junks forever and have NEVER been stuck like this before! I can't stop going back to the thought that the timing chain is shot! Like is jumping a tooth or something along the lines of that. I just don't have the funds with a house full of kids lol, so I really just wanna fix what needs to be fixed.

Thank you so much! This is driving me nuts and I really wanna get it figured out. I really hope I supplied you with enough information

Dave Ruckoldt