If you are self-funded, you will probably find many doors are open.
The best advice I could give would be to treat the whole process as a two-way interview. You don't need to be too afraid of rejection or sending a bad proposal, what you do need to worry about is paying a small fortune for a supervisor that doesn't engage with you leading to a drawn out, isolated part-time PhD.
That said - strategically - consider sending the proposal to a few places that you're the least interested in first. If you get no answer or negative feedback (or even positive suggestions), you can take this onboard before sending it to the places you're most interested in.