I would say July is a little late for Mayo. Everywhere else seemed to be fine, but because the interview season is done by December there, the whole process seems to move much earlier. I took the MCAT in July (end), which meant my scores were not ready until Sept 1st. I submitted AMCAS in early June, so everything was done pretty early (minus MCAT). I had my letters of rec pulled here, which took about a month for Mayo to process, and then they said that I was a little late in the season to get an interview, that it became much more competitive as the season went on.
Just my two cents- not sure how late in July you are talking. If its possible for you to take it earlier, and Mayo is your top choice, you may want to consider it. Best of luck!
Call the office- they are SUPER helpful (definitely among the nicest of admissions staff I've spoken with)