Thanks for your thoughts, but I figured it out...well, stumbled on the answer, to be honest.
If I save my files as .m4a rather than .mp4 they play through AirPlay.
Whew... The upgrade from Audio Hijack Pro v 2 to Audio Hijack v 3 has been ridiculously frustrating!
More: I guess those files being "MPEG-4 video" explains why they wouldn't open in iTunes, which doesn't have a video component, but opened in VLC and QuickTime Player, both of which do.
