i know your schedule is super slammed, but is there any way you can take a full, timed practice test? i feel like that you help you get a solid baseline of how you're performing now + to identify any potential areas of weakness you may have. it also could help you get a clear idea of how much time you'd need to spend studying btwn now and june 👍

best of luck! you've got this :)

as someone who's applied for a lot of competitive fellowships/scholarships (some that need 5+ LORs for a single application), i can tell you that your profs almost certainly will not mind refreshing the letter! if someone already likes you enough to write you a LOR, they're generally also invested in you and your success. they probably will not mind updating the letter with a new date and an added sentence or two.

if (and that is a v big if) you end the cycle unsatisfied and are planning to reapply, i would just be send an initial email thanking them for their time, sharing your results, and notifying them that you are preparing to apply again next fall. i would then follow up a little bit later and ask them if they would please consider updating + resubmitting their initial LOR.

ymmv, ofc, but i've been told that it's easier for a prof to update an existing letter than crank out a new one.