Aaron, at no time should you have constant vacuum going to the distributor.
If that's how you run it, the engine is constantly running too far advanced.
All vacuum advance distributors should be to PORTED vacuum. Otherwise just disconnect and plug the vacuum line and power time the car and leave it alone. You will have less timing than if you run constant vacuum to the distributor.
Also, silly question? Did you adjust the valves or have the spark plugs wires off and maybe 5 and 7 crossed? The popping out of the carb is not normal or good. Either 5 and 7 are crossed or possibly a cam lobe is rounding out. Hopefully 5 and 7 are crossed.