welcome back Dan
you will be able to run both 10k events in June
simply do week 3 after the 1st 10k race, and replace the Tuesday session with 3 x 5 minutes fast @ projected 10k pace with 3 minutes easy in-between
this is meant to be a return to feeling good session and not a marker as a training session
depending when the race is, Saturday or Sunday, you do the 6 x 1 minute fast / slow as normal 2 days before the event
ps.. was the 81 minute 21k close to your best?