You should be able to start and run without the FPR hooked to the vacuum. Just plug the line. The FPR is only there for adding fuel pressure under load.

You should be able to check the diaphragm by sucking on it with a good hose and plugging it with you tongue and see if it holds vacuum. Gas could have been coming into the intake from the vacuum hose. Hope you don't get gas from the rail or tank! Yuck!

If the FPR was stuck open and bypassing "ALL" the fuel to the tank it would starve. Under load, it bypasses less fuel to raise the pressure on the rail. Less vacuum more fuel.

Fuel is getting into the intake manifold from the rail some how? How long do you crank this thing to get that much from a cold start situation?

You could pull all the injectors. Lay them up and check for leakage. If it has a cold start injector pull it out and plug the hole in the manifold which is probably the first and easiest. Run the engine.

Find the fuel route to flooding or the reason for low starting fuel pressure.