Furring Basement Ceiling

I am planning on drywalling my basement ceiling. I have two 1/2" water lines running below my joists so instead of rerunning those lines, I've decided to fur out the joists. I'm just wondering what the best way to go about this would be. What size wood to use for furring? Run the furring across or with the joists? Really any advice would be appreciated. Thanks!!

 

Minimum would be to use 1x2 and extend onto the existing joists. I have done it that way without later issues at least. I would also cover the cold supply with foam pipe insulation for sure but it makes sense to do both. Most basements don't have enough height to lower things more than that either by using 2X for example. Not sure about code but you may need or should also at least protect the copper behind the wall board further with a steel plate to avoid anyone driving a drywall screw into the pipe now or later. I never tried strapping by going across the joists but most of that wood is not very straight and it would probably add more unnecessary waves in the finished drywall. At least when screwed to the joists tightly the result would be similar to just using joists as good or bad as they are.

 

Would re running the water lines to a more safe position be more or less expensive than furrng the entire basement? You may have to use 2x lumber to fur it with, since any couplings would be wider than 1x lumber, and you need to protect the piping from penetration.