Does you car have D jet ( wires running to each injector ), L jet ( wires running to each injector and a electronic air flow meter before the throttle body ) or K jet ( mechanical inj, no wires to each injector) ?

D and L jet can have a stuck open injector but the car should still run.

K jet uses pop type injectors so a stuck open one won't cause the problem you have.

D and L jet sometimes use a fuel pressure regulator that looks at intake manifold vacuum. If the regulator diaphragm fails, it can allow fuel into the intake causing a no start and eventually fuel in the oil. Pull the vacuum hose and look for liquid fuel.

All 3 systems use a cold start injector, this can be leaking / electrically active for too long when cranking. ( it typically turns on for a few seconds at sub 40* F temps from what I recall )

Too high fuel pressure can only be caused by a kinked return line.

A failing head gasket won't cause the issue you are having.