I have not seen it but why can you not pull other cables using the current ones even if it's say only one of them?
A long cable from the master is the best option.
Did you have an Openreach engineer do your BT Infinity install?
The original telephone cables likely go through the wall and under the floor and clipped in place. Plus their likely to be daisy chained so if you use one of the telephone cables to pull another cable through you'll break the link that joins the extensions to the master.