Yes, I see the problem with getting under it to work the faucet as it looks like it is on top of the fresh water tank and likely other stuff as you mentioned.
There is a good tool to take a peek at different parts of the RV here:
It lets us get an idea of what is hidden in the walls and all those out of the way places!
Click this snip to get a better view of what it should look like under there.
But that does bring up a problem about the leak. On the faucets I've seen, when they have two lines that go up into the center pipe with the big nut to attach it, those lines are usually soldered/attached up inside that center piece and a leak there is one, I've never found a way to fix as it is up inside!
So maybe be certain it is a leak from those tubes.
Is it at all possible the leak could be other places where it could be fixed?
One tricky leak can be water spilled around the faucet above the sink surface and work it's way under and come out below? Any chance of that? that might be as easy as adding some caulk at the joint between faucet and top, then tighten?
Or any chance of you seeing water at the joint where the built-in faucet tube meets the RV plumbing, rather than up inside? Any chance of reaching those two joints to verify whether it it a leak at the faucet or maybe lucky enough to be at the connections? Unless it has been really abused, those tubes at the faucet are usually pretty safe if not twisted or bent, etc.
Not worked on one of these, so just looking for anything that would let you fix it without having to do the BIGG job of getting it off!!
Can't say I have any better ideas but there is a tool to be aware of, if not seen one before. It is made especially for getting to the nuts on the bottom of faucets like this. Called a "basin wrench", they are lifesavers when needing to do that trick and about the only tool for that job.
Something like this is almost "required" for sink work!
Sorry! Remote plumbing is a tough one but maybe some ideas to kick around?