I'll keep this brief. It was a bitch to troubleshoot and maybe I can save someone else some hassle.
I was having intermittent problems with all sorts of wireless devices. Poor Wi-Fi performance, non-working Bluetooth connections, cordless cellphone interference, and non-working low-frequency wireless signals.
The culprit? An offbrand (Costco) LED lightbulb installed outdoors, over my front door. When I got replaced the bulb, all off the problems disappeared. The bulb appeared to be working just fine, but when I finally suspected it might be the cause, I noticed it was running far hotter than usual. Almost too hot to touch, which is very unusual for an LED bulb. However it was failing, it was apparently emitting heavy interference.
If you've reached the end of your rope trying to track down a similar problem. Check your bulbs. Seriously. And this is not the first time I've been bitten by this, a few years ago a CFL bulb crippled my TiVo's remote so you'd think I'd have known better.