Loss of Power During Accel/Popping Noise Under Hood

I feel bad asking yet again another question here, but I am trying to learn and fix my issues without spending thousands at a mechanics shop every time I run into a problem that's over my head. So here it goes.

I bought my 1971 Mustang 302 C4 Coupe a few months ago with some known issues, mostly cosmetic but a few mechanical issues. The P/O did quite a bit of work to get the car running since it had sat in dry storage from 2007 to May of 2021. I'll put a list at the end of this post.

Now my current issue. The car usually cold starts pretty easily with only some minor hiccups every now and then. I give it three pumps of the gas, and then pump the gas while cranking and she starts right up and stays running so long as I give her a few mild revs. I didn't pump the gas while cranking until the colder weather came (I'm in CNY so it's pretty chilly in Oct.) and without doing so the car would sputter out within seconds. So now the car is started, I let it warm up for 2-3 minutes in the garage and then pull out of my driveway. My road has a slight downgrade so it usually isn't necessary to give it much gas pulling out of the driveway. I live on a short road connected to a larger main road, and I typically coast down my road until the stop sign. Once I pull away from the stop sign, I start accelerating and the car just sputters and I lose all power for a second, and it roars back to life. If I don't take my foot immediately off the gas, the engine shuts off. I've kinda got it down to a science at this point. The car usually doesn't do it again during my drive unless I'm idled at a light for an extended period of time.

So that's the first thing it's doing. The second issue (which I believe are related) is during acceleration. If I push the gas pedal maybe 1/4 of the way down, the car accelerates perfectly, but if I push it down more than 1/2, all hell breaks loose. I can feel the power stop reaching the rear wheels and the engine makes this terribly loud popping and banging noise. The only thing I can compare the sound to is pops and cracks from a tuner. Don't misunderstand though, these sounds are right from the engine bay, not exhaust. So I've now got my foot all the way down on the pedal, car is popping and banging, I release my foot back to around a 1/4 and it feels as if the car just found its groove. I really don't understand it.

So here's the work that myself or the P/O has done:

-Radiator (me)
-Thermostat (me)
-Starter Solenoid (me)
-Fuel tank and lines (P/O)
-Distributor cap and rotor (P/O)
-Ignition points and condensers (P/O)
-Ignition coil (P/O)
-Carburetor(P/O)

I would also like to note that I tore the mufflers off this car, but the issues I explained above presented themselves wayyy before the mufflers came off. Before you judge, I'm redoing the exhaust this winter so I figured I'd have some straight-pipe fun for a month or so...why not? P/O believes the carb is running rich and the timing is retarded. I have no marks on my harmonic balancer so I'm not in a position to check the timing with a gun. I can tell you that the distributor is rotated in the direction that advances the timing. As far as the carb mixture, the car smells very gassy and has terrible gas mileage. Something else to note is the PCV valve doesn't sit properly in the oil cap and might as well be non-existent. A new oil cap and valve is in the mail.

Thanks so much in advance, I apologize for such a long post. I'm just trying to figure this issue out and unfortunately it's way out of my league. As a 17 Y/O, I just don't have the experience to diagnose something like this. Happy driving