What's the right tool for painting joist bays in my basement?
A true paint sprayer (spray gun, air compressor, etc) is the fastest option in nearly any household painting project (aside from trim).

The airless systems that run via electricity like the wagner system isn't nearly the same thing. I used that system to paint our picket fence and while it was faster than brush alone, it wasn't THAT much faster and not nearly as fast as a true spray gun would have been. 

So, I suggest that now is a perfect excuse to invest in a serious air compressor! ;)