Hi there, Tillyfan.
First of all I do hope you'll be surprised with an acceptance from one of the remaining programs.
However, if you do decide to reapply one thing I'd strongly recommend to you is to email the departments you were rejected by and ask if they could comment on what would make your application a stronger one for next year. Some of them won't answer, but even if one agrees to give you some feedback it would be much more helpful than anything we could say on this forum.
Some departments / admissions offices actually have an address in their FAQs for people who wish to know more about their rejection. In other cases, an email to the department registrar could do the job. In any case, I am sure that a well written (not reproachful!) email would get some attention from at least some departments, especially if you state your intention to reapply.
Best of luck!