Edit: let me preface this by saying that April would be ideal, but if you think you would do significantly better with a few more weeks to study, then consider what I said below.
I definitely support applying early, but let's timeline this:
- June 1 = AMCAS open
- approx. June 25 = initial primary data transmission
- early-mid July = most secondaries come out, first complete applications as people begin turning in secondaries
Since you have to be complete (i.e. secondary submitted) before most schools review you, I think as long as the MCAT result comes out before about mid-July, the OP would still be among the first complete applications that schools see. So as long as the OP still turns in the application early, I think writing the MCAT in May would be fine (or even June if he has his application already done and just has to submit).
Bottom line: as long as his MCAT results come out before ~15 July and he submits his primary/secondary applications early, and the time spent on application/MCAT is balanced well, he should be fine
Edit #2: you should also be reasonably confident of your score going in so you know where to apply before the score comes out.