If you could build your own cybernetics, how might you find a doctor that would be willing to install them?

find a list of doctors and call one at a time till you find one that will go for it, if one says that they are not up for it, ask them if they might know someone that might.

the compensation that doctors usually like is money,

it is the usual compensation for that type of thing as well.

the real trick to that sort of thing is to sell your ideas to them and see what you get,

you might be able to get someone to do it for free if you sell your idea well enough.

Read the cat-man article? Apparently doctors are not allowed to do that form of surgery, even cosmetic doctors.

You'll have to find a desperate doctor who needs cash for that one. So try newspaper ads.

Or if your creations are regarded as safe the try a research facility... Which can be located at universities and\or try online phone directories. They always help.