Adding perhaps 0.5% of extension to the existing cabling, using high quality copper cable and correct terminations will not have a noticeable effect on sync speed. The OP has been pretty clear that the modem cannot be placed next to the master socket, repeating it doesn't make it any more of an acceptable option.
In a previous house I put a couple of Cat6 outlets on the wall (boxed-in soil stack) right next to my master socket, and ran them up through the loft and down into the cupboard under the stairs using another conveniently placed boxed in set of pipes. And then ran a couple more back out of this cupboard into the living room directly above. The Openreach modem lived on the wall next to the master socket, and was patched into an AirPort Extreme. That's an ideal setup but not everyone can do it.