I have used Rover for years now. Our first dog was not friendly (with people or other dogs) and I was still able to find sitters that were able to accommodate her needs. My recommendation is to find a couple of sitters and ask for a meet and greet so you can explain your dog's needs in person and so you can see the sitter interaction with your dog. You can filter the sitters to find the ones with no pets and there are many of them that only sitter one dog at a time.
Have you tried Rover? I used Rover multiple times when i was traveling and never had an issue with finding exactly what i needed