Your house wiring is certainly way better than average! In your case I doubt that you have the third wire problem.
Ignoring voip for the moment, if you connect a normal corded phone in the destination room and connect it directly through to the BT line, press any digit to get rid of dial tone, do you hear any background noise? If yes, then the induced noise is getting into the cable either from the data rack or from an external source. If no, then noise is being induced into the OBi box within the data rack.
It could take a while to isolate the cause. Turning off all equipment in the data rack, then turning it on one at a time would prove that side of things. It would be interesting to site the OBi in the data rack and have only it and the router turned on, then plug a phone directly into the OBi in the data rack, then patch it through to the destination room and plug the phone in there.
It's all a matter of elimination! There have been cases of the OBi power supply inducing noise into the OBi itself, but I doubt if that's the case here as you say it's quiet when the OBi is in the destination room.