To answer your last question, there is not a problem with not having a current supervisor so long as you explain why. Certainly not having a long enough tenure with him or her is a good excuse. As for your profile, I think you should/could be competitive at any or all of your target schools, so if you find yourself constrained on time, and needing to reduce the number of applications, you might consider digging deeply into the schools' individual culture and deciding which ones seem to fit you best. Another strategy would be to split them up and go for 3 in round 1 an 3 in round 2, with your preferred schools in R1 so you won't have to wait for R2 decisions to pick a school (if you get offered one in R1 that is). Hope this helps.
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