When should I plan to take my DAT?

I know this question gets asked a lot and I have read through some of the other threads but each situation is unique. So as I understand it the application cycle opens June 1st. My last week of classes ends May 16th and I wanted to give myself at least a month (if not 6 weeks) of open space to buckle down and focus only on the DAT which would mean taking it mid or late June.

The important question is, will this put me in the late batch of applications?

How late will this put me and how...

When should I plan to take my DAT?