Hi Nick,
I think few people have made that kind of cable extension with a Solix. There is a risk you won't get any reply from the Solix people. I have some experience with older models; the M37, 981 and 999, but not with the Solix or Helix models. My units can operate with almost any configuration - no temp, missing channel, transducers from other manufacturers etc. Sometimes the unit will report something like "no transducer" on startup, but all my units can be forced to start manually. There should be such an option also in the Solix. I think you can omit transducer id and temp. You can probably make the unit operate properly with manual settings of transducer type, frequency etc after startup even if the unit protests.
I would start with a test. Connect all pins, except those for temp and id using test cables between the unit and the transducer cable and see what happens. (The pins may be tiny, so you may have to make your own test cables. I use pins from old computer cable connectors in my experiments.)
Remember, Cat rating of the ethernet cable doesn't matter, but shielding does. A well shielded and cheap Cat 5 cable will do the job as well as a new expensive Cat 7 cable.
Regards, Rickard