As far as when to apply, I'd start working on applications in July.
Another advantage to applying early is that you have more time to spread out your interviews and campus visits. Tomorrow I could have gone to interviews at 2 different schools or go to an open house at a third school. Since I just got accepted someplace, and have a major paper/project to do this weekend, I canceled. In two weeks from tomorrow, I just got a second interview request, and will need to figure out which one to go to.
My suggestion would be to go to the AOTA website,
http://www.aota.org/en/Education-Careers/Find-School.aspx and look up all schools within an 8 hour drive of you. That's so you can drive there and handle interview requests that are last minute. Make up a spreadsheet of all those schools, their due dates, how they want items submited, their requirements, any quirks, stats on admitted students. anything that matters to you. Pick 10 schools to apply to out of those. Yes, 10 schools, unless you have a 4.0 and 200 hours of OT shadowing. If schools have a low minimum GPA, assume that they will have lots of applicants. Also, keep an eye on the developing and applicant programs, and check out their websites. One school was opening an additional campus location. They had people apply to the existing location in OTCAS *before* the program had even been approved to go from applicant to developing.
Like the previous author, I also had difficulty on one of my references. I asked a professor who wrote me a reference last year (I made straight A+'s on all the assignments/tests) if he would write them again. Unfortunately, I contacted him the week before spring semester started. Even though I said I didn't need them for 2-3 weeks, a couple emails and phone messages went unanswered. I missed the deadline for one of the two in-state public schools I was interested in. I ended up getting another professor (who had me for two classes, not just one) to write a reference at the last minute.
So lesson learned there. Contact all references a month ahead of time of any deadline and confirm that they will be able to write the recommendation, and that they know how it will be submitted (electronically, they mail an envelope to the school, or they put the recommendation in a sealed envelope and give it to you.
Some schools want all components mailed to them and received before the deadline. One school had the requirement that all transcripts and recommendations go to me, and they are sent in together. That requirement meant that there was no way that my undergrad school, halfway across the country, could send the transcript to me in time.
One of my friends said that the reason he is a lawyer instead of an economist is that he couldn't get his Economics professor to write recommendations by the deadline for the PhD program.