One base, on stilts, constantly walking with the sun.
Going to need roads for that. Might as well construct rails. A circum-lunar railway! Probably want to build that at 80 degrees latitude or more, the trade off being solar angle vs material costs.
God, frickin lunar railways. Truly the future of everything.
And they don't have to be big. More on the scale of those little trains at fairgrounds.
If you build rails, you'll get a free good-enough conductor for getting power from the other side, even before you think about putting anything onto those rails.
How would a lunar railway handle thermal expansion? We’re back to the same problem that the nighttime lunar surface is mighty cold, and I’d expect big gaps to form
I have no idea how plausibly, but the book 2312 has a city on one of the hot inner planets that gets squeezed along a rail using thermal expansion. Even if that doesnt work, it seems like the sort of thing you could engineer around, just a more extreme version of the engineering we already do to handle thermal expansion.
Won't this throw up too much dust?
Then leave and wait for it to start sending us poetry about its constant mortal fear of the night :)