Bluetooth Unavailable When Running Dual Monitors

I have a Dell dual monitor stand and displays I connect to rMBPs via the dual Thunderbolt / DP ports. After connecting, Bluetooth becomes "unavailable." Tried Bluetooth plist, PRAM reset and all that other good stuff but nothing seems to work. I've tried connecting three different rMBPs to the dual monitor set up (two 15" rMBPs and one 13" rMBP) but that does not make a difference. It results in Bluetooth that is "unavailable." All three rMBPs are running El Capitan with the latest updates.

Anyone know what's going on here? Any fixes? It seems ridiculous that BT suddenly "goes away" in this fashion.