My daily driver is kaput!

Vehicle is a 1984 5.0l HO with rebuilt factory 4bbl carb. Ever since the exhaust was done there have been some odd issues. The car starts and runs okay when it is dead ass cold (i.e. I park it at 5pm, then start it the next morning at around 6:45a). Choke works. Once the choke finally settles down the car idles and runs fine.

So...my commute to work is about 30 minutes. I park my car at about 7:30a. I then go to lunch at around 11:30a. Car cranks up on the first try, but the idle is very low (500 or less). It won't stay running unless I keep my foot in the gas. After about 15 minutes of driving, the idle finally "levels out" a bit and the car will stay running at just under 750 (lower than usual). This pretty much happens 100% of the time if the car hasn't sat overnight.

Today the same thing happens. I get in my car to go home from work. Low idle, stalls a couple times, runs like shit, etc. The car starts running "normal" when I get off I4 and head through downtown tampa (still idling a bit low at around 750, and the car hiccups at speed). I make it to the middle of the elevated portion of the crosstown when shit its the fan. The car is still running, but when I hit the gas nothing happens. I coast to a stop and the car dies. I am able to restart, but I can't really drive much over 40mph in 4th gear...the car is hiccuping and running like shit the entire time.

I call it quits, pull over, call AAA, and open the hood. Everything looks good. Coil is hooked up, no loose wires...looks okay. The car will crank but it won't idle.

Car has new plugs, wires, cap/rotor. Has what looks to be the original coil and ignition. The carburator is a piece of shit rebuild that leaks a very very small amount of fuel out of the front bowl. All of the emissions shit and the associated vaccuum lines are gone or capped.

So what could be the issues? Need help ASAP!