"Could that minor voltage difference be the factor?"
No
Here is my guess for what it's worth: If I understand all this. There was ground to the socket because the socket in question showed continuity to another socket that had a lit bulb. There was power to the center contact inside the socket in question, according to you.
Therefore the bulb has to light
IF.
1.
IF Area of socket that touches bulb bayonet pins is clean.
2.
IF Contact spring has good pressure and contact is clean. The spring provides pressure for power AND ground. Pushing center contact against bulb tap and pushing bayonet pins against socket slots/sides. You need to feel a spring pressure when inserting bulb. If not, replace socket.
3.
IF Bulb is clean and tests good.
Therefore; One of the above was fixed, or temporarily fixed, by your fiddling/cleaning, cycling the contact spring.
All in all, you did as good as anyone could. It was/is one of those frustrating electrical issues. Systematic troubleshooting is all you can do. Reasoning it out after that.... and then magic luck
Warning: Not sure how socket is attached to housing. If it is "clipped in" using fingers or crimped on, that is a place to lose ground intermittently. If socket it soldered or otherwise integral, may not be a problem.
