Yeah I'm sorta running into the same problem. My problem is my semester is pretty intense and I am finding the extra time to devote to studying DAT AND study for my classes. I'm starting with learning PAT (since I think it is sortof fun and I am waiting for the rest of my study materials to get here for the basic sciences...). I don't really have any advice except make yourself do it!
I would suggest you start studying if school will interfere one week after school finals. Study for 6 weeks, submit your AADSAS early and you should be fine
I know how you feel... I just can't get motivated for my test in mid March. I "started" studying over Christmas break and am glad I did so because I haven't had any motivation. The only thing that did get me motivated was that I looked at my practice DAT this past weekend and saw how terrible I did haha. Now I'm ready to hit the books.