End of July is more than sufficient time. If you start cracking hard now, I don't see why you couldn't be done the DAT around July 4th.
Are you locked into Kaplan? How fresh is the course material in your head?
You should head over to Datbootcamp.com and do some practice tests as a diagnostic and gauge yourself. If you're already hitting 20's because you know the material well, you can jump into Achiever and TopScore and just work PAT and practice exams. IDK how much Kaplan will help considering there is quite a lot of more useful material for far less money. You can get Cliff's, Chad's, Crack PAT, both Destroyers, Achiever, and Top Score with money left over to grab a filet mignon, bottle of Glenlivet, and your first dental school application for about what you're paying for Kaplan.