Agree with B RON CO completely. Even if it's not precise, get more advance into the timing. You're not going to hurt anything even over adjusting it while you're just idling and trying to get it running. Only time too much timing advance hurts is under load.
A few more thoughts:
Professional Rebuilt edelbrock 600
This is what got me on the choke line of thinking, but there is nothing in the books that says even a brand new carb can't run like crap now and then. Even more likely on a rebuilt unfortunately, but you just have to deal with it, track down the gremlins wherever they are, and get rid of them one by one.
While they've been mostly good in recent years, the HEI's can suffer from bad modules like any other electronic device. Used to be a big issue with them, but not so much lately. Still, the possibility can't be ignored...
And absolutely check the firing order. Was the engine rebuilt by any chance? A new camshaft by any chance? You know Ford firing orders come in two flavors, right?
Electric fuel pump new with regulator
Not likely to be the cause of your current running issue, so you're likely good there. But future issues that are hard to trace can definitely be failing fuel pumps AND failing regulators.
How many pounds is it set for? Did you take a gauge reading too?
It will start, runs super rough with idle surging and have to keep feathering gas to keep running
Back to a previous question, did you rebuild the engine? If so, new cam? If so, did you do the absolutely critical cam break-in procedure? Sounds like that would have been a problem due to how it's running, but if you did not and are fighting an idle/running issue, you are very likely going to be buggering up the camshaft and lifters.
Not to be Dire-News Dan, but it's a fact of life and a problem with new engines unless you're aware of all the ins-and-outs. If you are, great. But if not, that's why we bring it up here fairly often.
Vacuum port on intake manifold is plugged
All of them? And all of them on the carb, including both of the large ones front and rear?
Fresh gaskets on carb and intake
I'm thinking vacuum leak but can't seem to find it
Was wondering about this too. I don't think this is as big an issue on Edelbrock/Carter carbs as it is on Ford carbs, but did you compare gaskets to their mating surfaces just to be sure they're matching? A mis-matched carburetor base gasket is probably the single most common cause of the larger vacuum leaks.
Again though, usually on Ford carb setups.
Good luck. Hang in there!
Paul