SL; that is a lot more info to go on and aid the discussion, your solution is in your facts.
1) First on the vented tank, my 66 probably has a similar tank. It has the filler neck vent that curves down and vent the tank all the time. The cap is not vented. Works great. If you have the neck vented another vent is not the answer. a vented tank is not holding any vacumn. The slightest leak eliminates vacumn. Gas does build a vapor pressure, an slowly vents out that tube, very minutely. the vent must be clear. but I don't understand the coiled 3 feet of hose around filler neck? so is that the correct gas tank with filler neck vent? if so that vent is enough. more vents won't matter.
2) you changed the carb with the same problem recurring, unlikely a flat problem, not impossible they were both identically wrong, just very unlikely.
3) you changed distributors and the problem is recurring, and you had the timing curve set. Again the distributor and Timing unlikely culprits...
4) But in your facts today you say the fuel pump goes to zero and the car still runs......The fuel pump pressure should not go to zero. it should maintain a regulated pressure, a constant pressure, from the regulator, that the needle seat on the carb regulates demand for.
5) You said the pressure gauge might be wrong, well it might be right as well.
6) you can change the gauge if that is a concern and re-check. So what would cause a electric fuel pump to drop out? one answer is electric problem from the wire feeding the voltage and for the grounds for that pump. Of course bad internal wiring as well. So if this condition happen with a mechanical pump before?
7) you had an engine rebuild and a tank removed and when that is done ground straps must be re-installed, near the coil, near the front fender and back near the tank maybe some others. Good solid new clean groundstaps, is a starting for electrical gremlins.
8) Heat causes resistance in electric wires and copper windings, that is why guys have so much trouble with starters near exhaust manifolds, the heat makes resistance in the copper windings of the solenoid, click, click.
9) when your car heats up, resistance can build up in a wiring circuit, and in your case since the fuel pump PSI drops to zero that is the first place to look.
10) Turning left could cause a loose connection or ground to move or be jostled by the suspension. other places this can happen should be looked at as well.
11) one really weak place is on the drivers side of the engine a metal heat tube runs down vertically near the exhaust manifold, the wires to the starter and eventually other feeds, run thru there. This is a weak design and the tube works as a heat stove and cooks the wire harness. it develops also a melting of the insulation, say at the bottom where it chafes on the hot tube.
As it sits straight down the now bare wire may not hit the tube,...but when it all heats up and resistance builds fast and you turn left,...Bingo it shorts on the heater tube, instant stall. The car can be restarted once the wires cool and drop staright down again, usually after the wrecker has left you at home.
12) so just a good place to check visually from the bottom, put it on a lift and look at it, but you can also just push the harness down an inch, for one test and pull it up an inch for another and secure it temporarily with zip tie or tape and see if there is any change, by changing the wires position from where it may be bare, it could help you locate such a problem.
13) Ignition switches with high resistance and loose contacts can also do this, when they heat up resistance builds, loose contacts can exhibit on left turns.
14) Sounds like your timing and distributor are good, but the wiring to that matters tremendously. Pontiac Jim mentioned the ballast wire and a full 12 volts needed. That is critical and the wire can do just these symptoms, it provides the designed low voltage for points, but when it is jostled in a turn and heated up from driving, it drops one more volt and kills the coil....especially if that wire is just haphazardly laying on the back of the hot engine....You must verify that the ballast resistance wire in the original car has been addressed, and fixed to provide a reliable 12 volt feed to the coil.
15) look back there behind the dizzy, is there a white cloth covered wire feeding the distributor, if so that is providing reduced voltage...unless it goes to a relay. if you have that you have to deal with it, ez fix is a relay. So a good place to look.
16) Fuel lines could be kinking, suspension crimping a gas line on turns, lots of things. but here are some basic checks.
17) I for one cannot see how a gas tank already vented at the filler neck would benefit from another vent at the gas cap. Modern electric fuel pump systems work off a sealed vacumn system. they maintain vacumn all the time, it is only vented to a charcoal cannister in the engine compartment for emissions, those vapors are then sucked into the intake when the car is started.
18) when you put an electric fuel pump on you have to know from the manufacturer of the pump how the system is designed to work,.. that is with a vented tank
or with a vacumn tank?
19) if you use the original designed vented tank with a pump designed for a vacumn tank,....well you will stall out, maybe on left turns.
20) The mechanical pump was designed to work on a vented tank at the filler neck tank and a no vent gas cap. It builds no vacumn, it is vented, so unless the vent is blocked, there is a slight gas vapor build p in the top of the tank. Just like when you open a gasoline safety can, you here the whoosh, that is the vapors escaping from the can, not vacumn. Vapors create positive pressure, vacumn is the absence of pressure. When you open the cap on the original design you can here a slight pressure, because the pressure build up is more that that tiny vent can totally dissipate. If it was larger it would seep gas vapors out in your garage and the pilot light on your gas hot water heater would cause those vapors to explode and blow you out of bed and into your neighbor's pool.
(So as a side note only store gas in your garage in a safety can, not plastic, not a cheap metal can that leaks vapors, but a safety can
. Pay for one, they cost more, it has a spring loaded lid and a cork seal and a flame aresstor in the neck, so when you drop it while filling the mower, it seals and won't explode or let the flame travel up the liquid column. Sorry just don't want to see guys blow up their Lemanses!)
21) SL you will get this, proceed methodically by tacking one issue at a time and making some notes and moving to the next.
22) I would start with what that electric pump system requires in the tank, once that is right I would explore the electric to that pump, it should not drop pressure, and just because the car doesn't immediately die is not an indicator necessarily and with a carb the float bowl maintains some gas, so it the pump restarts it mat still run, a modern fuel injected car would die and the pressure in the fuel rail is maintained without reserve.
you will get it as perseverance always pays off!