Good morning everyone, I'm gonna use this to try to answer most of the posts. Thank you so far for all your advice!
First off, I have a physical hard copy of the FSM and Body/Electrical assembly manual. The issue is that it only talks about tuning the OEM carburetors. The carb that came with the car is a Holley 500 CFM Performance 2BBL Carburetor. I tuned the float & fuel-air mixture using a general guide. The engine sounded leagues better after that tune-up. I then kept messing around with the air/fuel mixture to get the best vacuum pressure. Maybe that's where I went wrong. One thing I also forgot to mention before was that I replaced the sparkplugs and distributor wires so I'm pretty sure they can't be the cause at all. Used FSM to make sure I got the right sparkplugs.
I'm planning on pulling the tank soon, I know it needs a replacement because it leaks. I think it might be that the seal around the sending unit is rotted.
Before I cold start the coronet I always give it 3 pumps of gas before ignition. When the engine is hot it fires and runs like a dream.
I'm not sure why it was there either. The guy who owned the car in the past has done some weird things in the engine bay. I removed it and swapped it out for a fuel pressure reader valve. I just noticed that in the mornings the fuel pressure went to 0. I think it could also be the diaphragm in the pump is worn out. Fuel could be leaking back into the gas tank. It could potentially explain why I have to crank it a bunch to get fuel back up to the carb.
Here are a few videos I took (hopefully video links are allowed). I couldn't get many because shortly after this my power steering return line decided to rupture on me
(In most of these you can hear how the engine tries its best to stay alive)
Another cold start:
I'm not sure why it's so quiet in this one but this is another example of the engine trying to stay alive.
If it's able to run for about a minute it has no problem firing up again and it begins to sound way better than these initial starts.
Here's what the exhausts sound like right after a cold start: