I am in dental school right now and an email was sent to all the students a month ago. It was about AF HPSP and it stated that the deadline was July 29th too.
However, that's only regarding the three year / two year scholarship.
It does seem it is a bit weird for the 4 year scholarship deadline to be so early, but it wouldn't hurt to start early. The AF lets you do MEPS after selection anyways so you can probably get a lot of the stuff done by July 29th. It'd just be sending in your transcript, resume, LoR.
If I were you, I would apply to other branches too. Especially since the 4 year AF scholarship seem to range from 0 to no more than 10 depending on the year.
If you got other questions:
http://forums.studentdoctor.net/threads/c-o-2021-hpsp-thread-army-af-navy.1204873/