Been having trouble charging accumulators inside factory buildings, my main problem being that they don't charge, but am also starting to think that they may still be draining power from my base. Is this intended? Or am I doing something wrong?

Accumulators don't work inside factory buildings because power is transferred using hidden accumulators and accumulators can't charge each other. The draining part may be a Factorio bug. Accumulators will work properly in the overworld though.

Might there be a way around this? It'd be nice to be able to store power inside of a mobile base instead of having to constantly generate it with steam power. Y'know, place it down next to a few (dozen) solar panels to charge, and then venture off into the wilderness as a nomad, without needing a constant supply of water/steam.

The issue aside, I like that idea of a roaming power base. The largest tanks store like 350K water. Couple of those & a steam setup and it'd last for ages. Might stick one of these in my storage warehouse that I always travel with. Just plonk it down next to a pump output every now & again to top up the water and it'd at least have permanent lighting wherever you are!

To take the idea further, could then have a BP for a load of laser turrets to surround it and just whack that down on top of the warehouse whenever i'm starting up a new base. I like this idea!

while you cannot use solar/accumulators in factories, you can use steam power. i use bobs power mods and build top end steam power large buildings. with recusions and the advanced mining tools mod which allows you to create resource patches, i build small buildings inside with coal, setup miners, then belt out the next size building where i have a full steam engine setup. for water, i use the better offshore pump mod which upgrades the basic pump to put out more water and does not require to be in water to use.

I super recommend using waterfill and some nuke reactors in your factory buildings, waterfill means you can just have all the water you need and nukes mean you can with only a chest of uranium ore last pretty much indefinitely with 1 RPM in your pocket