OK, you watched a video on how to change a tubular flat in your garage or a bike shop, not on the course with the race on the line. The processes for the two are very different.
I have not seen the video you mentioned, but from your description, it seems like a great advice for changing a flat at home. I am going to help you with on the course.
On the course, the hard part is not getting the old tire off, it is getting the new one on. Luckily, since you have unglued rims, you can practice. Practice stretching the tire on by yourself, and inflating it. This is what you will do on race day…no gluing. After you get it on and inflated, pull it back off again. Rinse and repeat.
That will take care of your practice changing the tire.
So, how do you get the old one off ON RACE DAY? Brute force. Grab the thing, rip at it, pull it off. It is a tubular with a hole in it, and therefore trash, so don’t worry about it. Usually, this will get the old tire off. However, if there is a really sticky one, here is a little trick, just don’t tell anyone, it is a secret.
Tape a razor blade to the bottom of your saddle. If your flat tubular (remember it is already trash) won’t come off, pull that blade out, cut the tire straight across the tread, as deep as you can. You basically want to cut the tire all the way to the rim. Now, stick your finger in the tire, and pull. It will come off.
Now, pop the new tire on, just like you practiced. Don’t worry about all that residue stuff in the race, it is fine. You can clean it up when you get home.
The spare you carry with you should have a base coat of glue on it. Just put the glue on and let it dry for a few days before you fold it up. This glue, once heated by using your brake, will stick to the glue left on your rim by the old tire. It isn’t as nice as if you had just glued it up properly in the shop, and I wouldn’t go racing a 4 corner crit on it, but it will get you home, or to T2. Just take it easy on the accelerations, decelerations, and cornering, and most importantly, remember to fix it when you get home so you don’t forget and show up at your next race with an unglued tire.
Your other option is to ignore all of this, and use Vittoria Pit Stop, which works pretty well.
Tubulars are easy, those clinchers on the other hand, what a pain.