randomb - after being complete at most places in late july/early august, interview invites for me came in starting in late july and going through october, with most of the invites coming in late august and throughout september. the SDN school specific threads are a good way to find out when invites start going out. you could also check out mdapps (a lot of people keep detailed timelines for each school). many of the schools that i applied to started out by inviting people chronologically in order of their complete dates, so september invites went to the people who were complete in july/august, etc. and many schools go back and re-review you at a later time if you're not in the wave of invites that corresponds to your complete date, so i think it's advantageous to apply early so that you may potentially have many chances to be re-reviewed if you need them.
waiting for may grades to send a transcript to amcas is fine - remember, amcas doesn't send out your primary to medical schools at all until some set date in late june (this year it was like june 24th). so being verified in early june is completely unnecessary.
if anything, LORs are the hangup... getting professors to turn them in on time, or getting committees to send them out early in the summer, can be difficult.