@MrRooni We did put in a bracket, it was a slick kind of thing that in theory you can do entirely from the bottom side — sort of like a towel bar with a hexagonal shaft, and you put it up through the hole, then go perpendicular, then rotate the shaft to expand like a curtain rod between the joists. Then a bracket with screws comes down to hold the box. But I needed to run a ground wire anyway so did it all from the top.

No changes on the wiring, it's already a three-way. Just use the chains.