A ceramic holder would be ok but I think the regular plastic should be too, that's what I have in my after market and no problems.
Your old connector was loose, it melted around just one of the pins.
Notice the colour of the lamp pin compared to the one adjacent, looks like it might have been red hot.
BTW, no I don't think this caused the regulator problem, the headlight would be drawing less current with a bad connection, I
think it's very unlikely you would get a short there.
Replace the bulb and holder, you will be as good as new.
Same problem on a 2000 v11s, Just bought a new plastic connector at auto store. Problem solved.