For sure, and that can definitely work. But, you will need three times the number of solar panels (since half the time the panels are doing nothing and if you're storing a lot of energy, that means there's a proportional amount of storage losses.)

And I honestly don't know how much mass in batteries would be needed for 15 days worth of storage, but my instincts say too much.

Keep in mind that total mass to deliver can sometimes be the biggest cost limitation. A nuclear generator that gets delivered in one launch could be cheaper than otherwise much simpler solar panels and batteries if that solution requires two or three launches.

Yeah, theoretically if your positioning is perfect you can get that eternal twilight, where the sun just travels across the horizon in a circle. But you know the moon wobbles a bit, so while you might get a month or two of straight sun, you might get a month or two of straight darkness, where the sun is just below the horizon, just barely out of reach...

Vacuum... everywhere?

Dyson furiously trying to replicate this phenomenon for their next vacuum

Yeah it was Mars that I was thinking about, not the Moon.

Pro: nothing's ever gonna kick dust on your panels except space debris or ourselves.

Con: nothing's ever gonna wipe dust off our panels.