To finally solve for this, I installed a set of 2.1 computer speakers under my bed, and I have my phone run a 10 hour recording I found of an air conditioner. The noise this generates sounds just like the real thing, and I keep it juuuust loud enough to drown out the road noise and upstairs neighbor's heavy footsteps. A click or two louder if their dog starts going nuts at 3am. I'd prefer actual quiet, but a low steady rumble is second best. Recommended highly.
That sounds like a fantastic setup. I wanted to rig something like that over the top of the bed, but underneath would be elegant. I can highly recommend 10 hour rainstorm sounds as well, similar noise profile to industrial white noise but has a more natural association for me
I use the Bose “sleep buds” which do exactly this but in your ears. After reading this article though, I wonder if such white noise is good or bad (my recording of choice, ironically, is train noise).