For one thing, check the audio specs again. It is probably peaking at -10 to -8 dBFS (minus DeciBels Full Scale). Digital audio units don’t go above zero, but analog does. You should be able to add a compressor/limiter effect to limit the peaks.
If you are not familiar with using waveform displays, the best thing would be to add a “broadcast limit” filter to the whole thing and hope for the best.
Check your field order. (should almost always be lower first for NTSC).
As you shot in 24p, check that you introduce pulldown correctly.
Check what codecs they accept. I’m guessing they want a DVD-ROM, not DVD-video. Native QuickTime should be OK, but confirm. Apple Yuv is universal, as is Photo-JPEG. P-JPG at about 95% quality will save a lot of space and still look quite good.
good luck with your submission.
-jeff