Is your fuel pump on in the first picture? That looks like an edelbrock 1405 600cfm carb. If so their recommended operating psi is 5.5 if I remember correctly. In the picture it looks like you are at 3 psi.
I did notice that for whatever reason, the mechanic that last worked on the car, swapped out the vacuum lines that go from the carb to the distributor. According to Edelbrock, the vacuum port on the front passenger side of the carb, goes to the distributor and the driver's side port goes to the automatic transmission. I swapped those back like they were supposed to be. I haven't started it up yet but not sure if that will make any change. They were correct before and was still stumbling.
That would screw up your shifts and drive line pressure through the roof at idle. The timed port is intended to go to the distributors vac advance pot(I would never put it there and don't get me started, lol) and the full manifold vacuum port is intended for the transmissions vac modulator. Get that sorted out and continue the down troubleshooting tree from there.
Actually the port on the front driver's side of the carb is capped off since the manifold vacuum port on the back of the manifold is hooked up to the line to the transmission. The way it was originally on the factory 302.
This. Just leave the vacuum advance disconnected and block of the line for testing purposes. Check total timing around 3500 RPM to ensure it is advancing properly, and then go drive it and check for the issue.
Not trying to be rude here because I've certainly been there more than a few times long ago. When it comes to this stuff knowledge really is power and can save you TOONNNNSSSSSS of cash through the years and over a lifetime of being a car lover. To avoid future tail chasing scenarios like this and many more to come AND end up with a better overall running engine, my best advice would be to study engine tuning so you can do some if this stuff yourself. Some basic handtools, manifold vacuum gauge, and timing light will be all you need to get started on learning how to diagnose and tune towards the engines optimum calibration. Fresh set of spark plugs are easier to read and never hurts the tuning process either. I'm pretty tight on time building my engine lately but I'm sure there are others here who would be happy to fill you in with details needed along the way. Can also dig up some pertinent resources to help you accelerate the learning curve a bit faster too. If it gets to a more time consuming technical aspect of the process you could even call while I'm out working in the shop. Have helped more than a few out around here through the years and phone support's usually much faster for everyone involved. Otherwise tuning carb's and ignition curves is becoming a lost art due to all the EFI/computer based stuff and MOST mechanics(best ones are usually a bit older and have a few very good running older school toys) don't know their asses from holes in the ground when it comes to modifying fuel/ignition curves away from stock(which BTW is a downright HORRIBLE TUNE for anything even remotely performance oriented.. and gives crappier mileage too). They(average mechanics) just set the tune to bone stock parts spec's and every modification ever done to the car gets pissed into the wind because the tuning is not optimized to take the greatest advantage of them. Just the simple addition of a free flowing performance muffler and nothing else changes the tuning requirement. If you don't have the time or getting sick of wandering through the forest.. might be much better off time and moneywise to just bite the bullet and take the car to a well respected chassis dyno tuner and tell him you want to work out "driveability issues". For between $300-$500 they will pick up where the regular mechanic left off. Just be sure you ask for PART-THROTTLE driveability tuning so they don't forget about that section of the powerband while searching for more peak power @WOT. They love cars that are way off their tune.. makes them look like superstars and the customers drive away spinning the tires to test out the newfound power they just paid to free up with ignition and fuel tuning.