By working with the coaches.

Figure out when the kids have athletics / other events and work out a schedule that has them missing as little as possible. Typically, those kids will have basketball, track, etc 5 days a week... It's not a huge deal for them to miss that once per week. That's how we always worked it out.

If you have an assistant, one person does the middle school sectionals and one person does the high school ones.

Any coach whos's reasonable will understand, especially if this is coming from Admin.