The only way to know if this MIGHT work for you is to actually sign up for a membership. Sign up for either the Standard or Premium level membership because: the Standard and Premium homeowner (Pet Parent) memberships allow you to search for sitters in their database, view their profiles, and see which sitters have “favorited” (bookmarked) your listing. You can try inviting sitters you find in your search but I have read here from other sitters they don’t respond usually. But you never know until you try.
If you decide to sign up, take time to make a really nice listing. This means SO MANY THINGS. I kept tweaking my Housesit listing as I learned more and more about using it to the best of my abilities. I found so much great advice here so you’ve come to the right place for some direction. In addition to whats already been suggested, I suggest the following:
Clean your house like its going to go on the market for sale. (This is what it should look like when a sitters arrives too.)
Put away the clutter on tables, countertops, sinks, dressers, etc.
Take AMAZING pictures of your home. Front of house, back yard or patio space also. Include a pic of every room the sitter can/will use. Sitters want to see a clean home, a place to work (desk, table), a nice bed to sleep on (not a futon/fold out couch). Also take several good close up pictures of your kitty. Talk about his good traits also, not just his negative ones.
Making a great Housesit profile takes A LOT of time and effort. If you put in the time and effort up front you will have a much better chance and finding what you seek.
I wish you luck in your search for a good fit. And thank you for rescuing a street kitty and caring so much about him. 
Write your profile in a pleasant manner of your expectations, not “barking out” orders making it only look like a one side is benefitting from this sit. List the responsibilities you expect the sitter to do. Make it clear if you want ONLY a female or if a couple which includes a female will work. If you are in a remote place or an area that requires a car to get around, consider letting the sitter use your care during the sit. (you can ask if the have a current valid drivers license and ask to see it if you like).
(Post edited by the Forum Team to comply with the Community Rules).