Found a solution!
PROBLEM: Ripped CDs play fine on the source machine, they will stream and download to other machines via iTunes Match, but they either: A) play partially on iOS, then go silent, or B) play and then jump to the next track while displaying the prior track. Very annoying.
WORK AROUNDS: A) Manage Muic without iTunes Match via USB cable or B) Download the tracks... they will still fail in iOS Music app, but they will play in Amazon Cloud Player app.
CAUSE?: I think the mischief begins by adding songs to iTunes by drag-and-drop or by having the iTunes Match scan in iTunes interrupted.
SOLUTION: What worked for me is the following:
1) Back up for safety.
2) Have an empty trash can... that makes it simple.
3) Locate the "Automatically add to iTunes" folder at the root level of your iTunes folder.
4) Delete the tracks from iTunes with the option+delete method and tick the "Remove from iCloud option." Have the tracks put into the trash can.
5) Quit iTunes
6) Open the "Automatically Add..." folder.
7) Move the tracks from the trash can to the "Automatically Add.." folder.
8) Restart iTunes.
9) Let iTunes do it's match thing, which may take a while. Do something else while it's running. Read a book, volunteer at an animal shelter.
<time passes>
10) Check out the new tunes on your iOS device. They play now!
Hooray!