For the ISDE, use mousses. Practice your technique and you'll get it down. With some practice, it only takes a little over 4 minutes to do a mousse.
FIM tires are garbage so it's pretty easy to start tearing knobs. Plus, if you put a hole in the tire, the tubliss system is done. I use tireballs for my regular riding, but for the ISDE you definitely want to use mousses. I had to learn how to do mousses at the ISDE (while under the time constraint - no practice) and was doing them in about 7 minutes, sometimes a little less, so with practice ahead of time you'll be fine.
Remember, you have 15 minutes at the end of the day, plus 10 minutes in the morning. I did tires and oil at the end of the day, air filter in the morning.