Finally some great tips. I appreciate your suggestions and will try some out. Have a great day!
Homosocialality is a strong motivator especially among boys, it is in their nature to be drawn towards each other, and have strong feelings of the need to belong. This explains athletics, military, mens groups like the masons... but there is also another strong motivator that we have...girls.
Also just the fact that so many dads push their kids into sports, is hard to overcome. Anyone can understand if the ball crosses the line- goes over the fence, or into the basket mentality, but most of the time we have to explain what we do, they don't know if a band is good unless we tell them.
Encourage fun games, social events, trips, that they can't experience anywhere else. that's the only way to compete.
Place a grade for all outside school sectionals and rehearsals. The students must feel that it's important to attend the sectional and a grade will do that. Yes, it's the easiest 100 that a kid can receive, but they should receive that 100 for being there. If you allow the students to not be there without a penalty, then they will always choose to not be there. I disagree with "Easy" below, students like to be good and they do like to work hard when shown how to do it.
Also, as the director, you must try to schedule your sectional times around their practice schedules. There are many times that I have to schedule two trumpet sectionals, one for 7th grade athletics and one for 8th grade athletics.
In the end, the kids have to see that you are serious about the sectional and you are willing to make it work.
Last, but not least, you need to keep building relationships with your coaches and your admin. It's up to you and the coaches to work out the schedule without the kids in the middle.