Apply as close to June 1st as possible with your current scores. Study for the DAT in the meantime. If you don't get responses early in the cycle, retake the DAT and let your schools know to expect the new scores.
Also, only retake the DAT if you can substantially improve your score. The only thing worse than getting a 17 once is getting a 17 twice. Personally, I used Kaplan DAT prep to study for my retake and it really helped. I've never used the other programs so I can't offer any comparison. What I liked about Kaplan is that they teach testing strategies for each each section, as well as review test relevant material. But that's all they do. And for me that's better. I don't want my 2 semesters of organic chemistry regurgitated to me in a review session, I want relevant concepts reviewed in DAT testing format. It helps filter out the unnecessary material, you know? I also recommend getting the extra math study course. The QR and RC sections are good indicators of dental school and board exam success, which is why they remain on the DAT. If memory serves, RC demonstrates a student's ability to filter out unnecessary information and retain what is important. QR demonstrates a student's testing stamina, which is crucial for boards.
Whatever you decide to do, you will be adding to your application and becoming a better candidate for dental school. As a reapplicant, I know it's very hard to stay committed or see how the application process can better us another time through. But sometimes that extra year or two really help you develop into a much better candidate and person.
Good luck!
PS
Don't burn yourself out studying. It hurts much more than the extra studying can help. Make sure you're rejuvenated, confident, calm (not just on test day, but everyday)