Jonathan, you use the FR 64 with the Lyra? Silver wire? Any other tweaks?
These days we are using the SAT, which has a captive tonearm cable.
But for any tonearm that uses the universal headshell system (including the FRs), the headshell contacts and wiring are a decided weak point.
The sound quality can be improved by providing each headshell with a dedicated wiring harness that is long enough to reach the phono stage, and made of thin Litz (or magnet) wire so that the tonearm motion is not impeded. Gently twist the plus and minus wires together, enough to avoid picking up noise or hum, but not so much that the harness stiffens and impedes the motion of the tonearm.
The wires should be secured at one or two locations along the tonearm tube, and another at the rear panel of the turntable plinth. Do make sure that the wiring harness is generous around the tonearm bearing - coiling it, arching it over the bearing, securing it to a "V" shaped recess directly above the bearing should all be suitable. The harness can be terminated in RCAs or XLRs, whatever is appropriate for your phono stage.
If you attach a small Velcro wrap around the arm tube, and a second Velcro strip or some kind of clip at the plinth rear panel, you should be able to secure and release the wiring harness quickly and easily.
When you remove the headshell, its wiring harness goes with it, therefore you will need a storage location with sufficient room to accommodate and protect both headshell and harness.
BTW, it may be safer to leave only the ground lead portion of a ready-made tonearm cable connected to the phono stage, this is to keep the tonearm grounded and prevent hum or electrostatic issues.
Mechanically the universal headshell socket again leaves much to be desired (even when using 2-pin headshells), but simply cleaning up the electrical system should deliver a rewarding upgrade to the sound.