SBC problems!

Ok guys this for the engine in my daughter's 77 Monte Carlo. There appears there may be several problems, but I am perplexed. General story, and I will try to upload a video of it running. Engine is a 305 with an Edelbrock 550 cfm on dual plane intake. Carb was recently rebuilt by the local go to guy. It is cammed, , not sure of specs, but not real hot. Tranny is a B&M turbo 350 with a shift kit, standard torque converter. Has headers. All vacuum lines hooked up. New distributor -all new guts HEI. New plugs. Engines idles nicely at 600 rpms. Revs up fine, no real problems. Occassionaly will sit and idle for like 10 minutes, and then for no apparent reason, shuts off. Restarts immediately no problems. Sometimes will shut off again in a few minutes but not always. Early on put it in gear, takes off no problem. Drove it to local school about five miles away, overall ran fine, -really good at 80mph. Did a uturn in school parking lot, stopped and told someone there we were trying to get ready for a car show, and it cut out (quit running). Restarted, put it in gear, quit running. Did that four times. Began to crank a bit hard, almost like not in time. Then caught, started and gave it bit more gas, put it in gear, and away we went. Five miles back. No hesitation, runs great at 80, no problems. Slow down to make left hand turn into the driveway, it stalls out. Repeat performance of restarting like at school. Pull up in front of garage door, idles fine, no problems. Put it in reverse to move and park else where, it stalls out as soon as putting it in reverse. Does that 5 times. Becomes increasingly difficult to start. Coast backward enough each time I get where I want to be, put it in drive pull forward without it stalling shuts of as I get where I am about to put it in park. IN disgust take out keys and quit for the night. At the end of my skill set. Any ideas or help? Thanks. BTW we have named the Monte Miss Obstinate because it has fought me step of the way. TIA

Easy stuff first. My first thought would be heat soak. Is the fuel pump original?  Or how old is it?   Sounds like it runs great til you stop. I was then thinking maybe electrical, something with the power wire to the distributor maybe has a cut in it. Is the power wire original or did you run a new one to the fuse block. My last thought would be something with the idle circuit in the carb. I'm not familiar with Edelbrock carb so someone else would have to chime in.

My first thought is fuel supply. Good luck with it.

Hearing your different symptoms makes it difficult. Fuel to me would cause a stall but may not be so easy to restart. Electrical can have and open fault under heat, but may need to cool before working again as well. HEI ignition modules are famous for just shutting off, but usually take a while to restart. But if I to make a guess, it could be a distributor issue, between either the carbon bushing, the coil or the module. Fuel, I would lean more to the carb flooding. The pump would not seem to recover so quick if it was not supplying fuel.

The Edelbrock carb needs the floats set correctly. They also need an insulator of some sort from the heat. Either a thick gasket or a spacer.

I agree with bracketchev about the distributor, along with making sure the ground strap is connected between the engine and the firewall.