Sounds good time for a change!
Any chance you have an RV parts store near enough to make it practical to drop by?
There may be lots of options but it may take more a bit of looking to compare things like how much space is covered and then there is the question of needing to swivel to get the light to the best spot?
Does it really need to swivel or would a fixture that had a clear dome to let light go out to the side but extend down a bit lower, seem to work?
I'm not a big fan of halogen as they do burn hot and also use more battery than newer LED might, so I look for places to change then out.
One thing in your advantage is that finding one to fit physically will be good and no worry about a new LED using more power, making the electrical part no problem!
Maybe something like this?
https://www.recpro.com/rv-12v-flush-mount-ceiling-light-dome-with-switch/
What I'm getting down to is that I like to see this sort of thing in person!