OP - Besides Care.Com there is also
https://www.sittercity.com/ - both of which should have college students listing themselves as sitters about this time of the year. I also think American University has a sitter list you might use. Could you consider seeing if any of the para assistants would be interested in a summer job at your son's elementary school?
If I were you, I would want at least two references that you could call to see how the person was, interview the applicant and then have her/him come be with DS once or twice as you will need to show and share more about your DS with a new sitter since he is nonverbal. I think it is important to share information on anything which might upset DS and what the signs of frustration or distress would be. I would go out at least once and return early to see how things are going to be as certain as possible that it is a good match.