I agree with Drathaar that your converter could have been working. Only way to tell would be to connect a meter.
You're right, the jack is connected directly to the positive post on the battery and grounded to the frame.
I don't think the jack would work connected to the TV of the fuse is blown, but it is always worth checking. I blow that fuse at least once a trip.
Hopefully with a full charge the other gremlins will fly away.
I also agree if you won't be using the trailer for awhile that you disconnect the ground at the batteries.