Tall lunar pole towers: https://futurism.com/the-byte/harvard-super-tall-towers-powe...

Maybe better: nuke the moon and reduce a few key crater rims, then use much shorter towers. Could be that a series of regular bombs might be more effective and less likely to "alarm the horses (general public.)"

Maybe use solar panels to split lunar ice water in to hydrogen and oxygen, then use that to run fuel cells in the dark periods.

Given the satellites need to be geostationary, don't they have the same issue? I know due to the higher altitude you would get more time in the sun but I feel like even one to two days would be too much distruption (2 days battery storage would be crazy expensive to send up but maybe that equation changes one day)

Beam the power around the moon from where it's sunny at any given time to wherever needs it, using phased array orbital substation reciever-transmitters. No atmospheric interference to result in high rates of transmission loss. Might prove cost efficient.

Near the poles?