I'd say suck it up, apologize to everyone involved for the mix-up, and get those kids back in your group.
It is NOT worth sticking with the letter of the law on this one, because the point of everything we do is to make a good experience for the kids. Is it a good experience for them to be kicked out their senior year, and for your guard to not have a qualified captain??
You need to patch this up, because this could have a terrible effect on the entire year, and for the future. Those kids will tell everyone else to not be in guard, and you will have issues recruiting.
You also need to figure out what's going on with your guard sponsor that they can't get auditions figured out for only 10 kids. Or what's up with the judges that can't watch another kid audition while they are tallying. If you can't fit one kid in late while tallying for 7 kids, maybe there are bigger issues here.
I think you need to have a conversation with your guard sponsor, and then with those kids separately. Patch it up, take the blame, do whatever you need to do. This isn't worth it to stick by your handbook. You'll be lucky if those kids decide to come back.