Do you have a parent listserv in your area? I realize it makes it not anonymous but I’ve seen requests for this on ours and get some good recommendations so might be worth it. One other thing that could be helpful is reaching out to a place that works with issues more specific to your sons and even if they don’t have exactly what you need, ask for recommendations. For example, this eating disorder clinic in Montgomery county might have some good recommendations. I am not saying your son has an eating disorder, but not all therapists are very well trained in binge eating in my experience and the best tools to support kids/adults in that so I think finding someone with that specific background might be very helpful. a therapist who does not specialize in feeding stuff could potentially be harmful in that arena.
Here is the one I found, no personal connection but have experience with binge eating personally and have a mental health background. I read through their website and blog, and I find it to be aligned with what I know to be recommended. They work with kids 10+ and specify does not have to be an “eating disorder” and they aren’t focused on diagnosis. Lots of therapists and options. The therapy techniques they list are evidence based and ones I would want a therapist to use with my child. At a minimum of your child is younger or it doesn’t feel quite right they could at least provide some recommendations to outside therapies as they certainly refer out themselves sometimes.
https://www.theeatingdisordercenter.com/jennifer-rollin-msw-lcsw-c.html
Hope this helps! Good luck op.