The best way to do this correctly would be to relocate the master socket to the hallway. Officially only Openreach are permitted to do this of course.
My original ADSL setup had the master socket in the hall and my modem in the study running from an extension. Because my extensions are star wired I put a filtered faceplate on the master and ran the study extension via AB using a rat-tail filter as I advised earlier. This all worked perfectly well.
When Openreach later installed my VDSL service their helpful chap relocated the master to the study by using my existing extension wiring to take the line directly to the new master and then back to the old master location to connect to the other extensions. The joining of the line to my extension wiring was done using jelly crimps behind the old master socket.
This does require you to have at least 3 pair extension wiring (ie 2 wires for the existing line and then 3 back to the original location) for this to work. Luckily I did have such wiring in place.