It sounds strange to start with, and your idea may or may not work depending on exactly what changes the engineer made. Was he a true Openreach guy, or a subcontractor such as Kelly's or Quinn's?
I'm going to ask you a few questions. The answers may help the next person along.
What was the setup before FTTC? Was the one that now has the blanking plate in use as a socket, and was definitely the master? Or was it always a blanking plate, in which case are you sure it isn't just a junction box? A photo uploaded somewhere showing its insides would be very useful.
The one in the living room is now supposed to be the master. It must be an NTE5 for the FTTC faceplate to fit, but it isn't impossible some internals have been removed, or the "blanked" master no longer is a master, or you now have two, which isn't ideal.
This is why your idea, whilst fine, and in principle achieveable one way or another, possibly isn't as simple as you describe.
Incidentally, the VDSL2 line is not filtered. It carries everything that came in from outside. The filters are bi-directional and remove anything outside the audible range from the lines to the phones, and back in from those lines. To the phones because with the broadband signal on it you woudn't be able to hear a conversation, back in because any non-audible "noise" picked up by the wire has to be prevented from getting back in and screwing up the broadband signal in the same way.
The correct setup, that the engineer should have been able to do, would give you phone and FTTC in the office, phone only in the living room, and depending on what is going on at that intermediate box possibly a phone there if it previously had one.
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