If I were in your situation with a (no longer installed and now discredited) XNTE, I would do the following:
(1) Open the XNTE. Yes, that is permitted. Withdraw the yellow plug and consider how I might make a temporary connection to the incoming pair. Perhaps two paper-clips, sufficiently manipulated may allow good contact to be made to the left-hand terminals of the socket.
(2) Take a standard LJU2/3A extension socket from my grotto.
(3) Connect a short length of CW1308 specification twisted pair to the 2- & 5- terminals of the LJU2/3A. Solder the other end of the twisted pair to the manipulated paper-clips.
(4) Having identified the A- & B- wires of the incoming service pair (using a DVM, with the +ve probe connected to a good earth), connect my temporary test socket by plugging in the paper-clips.
(5) Perform all the usual "test socket" experiments.
I would also grumble, firmly but politely to my ISP/CP about the lack of a suitable test socket due to the presence of an XNTE. If you do ever manage to get an Openreach technician to attend, s/he now has the authority to by-pass the XNTE -- just using it as an external junction box, nothing more -- and to fit a standard NTE5/A within your home.
(My thanks are due to Black Sheep, for providing the information regarding what Openreach technicians are now allowed to do when attending a site where an XNTE is currently fitted.)
Regarding your noise issue, I would like to see a few day's worth of RouterStats graphs (for example).