6v to DC input jack seems to work fine?

with any of the others which input 11-13v, it got warm to hot.

Let's say that warm means temperature increase of 30c. The package has a thermal resistance of 100c/w (less than that actually). That means a power dissipation of 0.3w. At a voltage drop of 13v -> 5v, that means a current consumption of 40ma.

With the same math, assuming hot means temperature increase of 50c, you get a current consumption of 60ma.

I would have expected the load to be 20ma max and 10ma typical for your situation.