Last year we had a certified LD teacher tutor DS in study skills and organization. We hired her through the specialist private school where she is on the faculty, and the rate was $70/hr. He is doing better this year and is managing without her aid.
One thing that I would be sure of is not to go to the tutor's home if the tutor is an adult with younger children. We tried that one year, and found that we got what we paid for, $25/hr for a teacher to hand him the same sorts of worksheets that he got at school and have him do them at her dining room table while she ran around after her 4 yo. If I'm paying for a tutor I want that person's undivided attention during that time, and if I have to pay a higher rate to get it, then so be it.
In STEM subjects, I find that older boys (ms and hs) tend to do well with tutors who are nearly peers; just a few years older is good. It seems to help them to see that another boy who is not much older not only managed to pass the subject but actually enjoys it.
PS: Is your son allowed to do his math problems on graph paper? DS finds that helps him IMMENSELY; part of his difficulty is a handwriting issue, and the grids help him keep the numbers properly lined up. (Over the years he has had several teachers object to accepting math or science work done on preprinted graph paper, and for the life of me I cannot see why. Working scientists use graph paper all the time.)