Are you doing quant or qual research? For quant, I wouldn't spend too much effort or time on this. Focus on your theoretical model and hypotheses. I don't know much about qual sorry.

I would just send the proposal you have developed on your own, rather than tailoring your proposal to meet the stated interests. They want to review your work and get a feel for where you are at as a candidate. Also, the potential supervisor might be looking for new ideas. You just don't know. In short - be yourself and submit the same thing to everyone. If you want to add a couple references from the potential supervisor, then do that (providing it makes sense conceptually).