There is one major flaw in the method of throwing away the most "off" judge, because there will be scenarios where you cannot possibly objectively figure out who is the "off" judge.
For example, what if the ordinals for three judges are 1, 5, and 9? Do you throw out the first place or the ninth place? Or if your three marching scores are 2, 3, 4? Or your four music judges (I know this would be ridiculous) are 1, 4, 6, 9? I know when we see a judge put Bell or Duncanville 10th in music, it's easy to say whoa that is obviously "off" from the other judges, but that might not always be the case. If you're going to have a throw-away system where you're not counting judges scores, pretty much the only fair way to do that is to throw out the high and low for everybody.
A way to throw out high and low scores would be to add two music judges (five total) and two marching judges (four total) so after highs and low scores are thrown out for everybody in each caption, they'd still be weighted the same as they have it now. But you know there's no way UIL is going to pay for a nine-judge panel.
EDIT: Looks like steeldrum was thinking the same way and beat me to it! oh well.