I'm glad that this seems doe-able.
Would you be able to gove me a bit more info on this e-bay side mount that you have bought?
One of the reasons I threw it out there is the fact, that there are lot of very handy and skilled people on this forum, whom might be able to figure out some means of attaching the cleaning kit to the wire stock by either machining (or possibly 3-D printing) some sort of a jig or a clamp, which would secure this kit to the stock without having to use the tape or parachord.
I would like to start some sort of a brainstorming session on this, since there is a good possibility that there are already suitable products to accomplish this task freely available at just about every hardware store across the country with either little or no modification at all...
I just haven't thought of them yet.
If there was some kind of a lever clamp (not sure what the proper name would be), which would mimic the way the cheek riser attaches to the T81 SR, that would be ideal...but I'm pretty sure our collective brains can do even better?