Songs stuck "processing"

You know, I know there's not going to be a workable answer for this, having been watching the Communities re this problem since iOS 7 was introduced, but,

WHY DO PURCHASES OR MUSIC MATCH SONGS GET STUCK "PROCESSING" AND NEVER FINISH DOWNLOADING?

Ahem.

Symptom: Go to Purchased, and select some to download. Then go to Downloads, watch the tracks download and then halt at "processing." At this point you cannot edit to cancel them.

It got to where my iPad 2 would never successfully complete a download of any song (or podcast, which I assume uses the same mechanism). Bizarrely, in all other things involving network-to-file io (Dropbox, saving to Microsoft's Onedrive, iCloud sync, and, particularly strange, downloading app) it worked flawlessly. I figured something must be going wrong with the iPad. Attempts at solving the problem with Apple support and a visit to the Geniuses did not help, even after doing a factory wipe. Ok, something must be wrong with the iPad. It is almost 3 years old.

Finally, the screen stopped responding to touch and I figured, rather than pay to have the digitizer replaced, get a new iPad. That'll fix it, right? the iPads on display at the store sure are able to download purchased tracks. (Yes, I stealthily logged on to iTunes on a store iPad, downloaded some. Worked perfectly. In the meantime, my own, in the same store, continued to fail, so it's not a problem specific to my router. I've tested with other routers, and with 3g, anyway).

So, new iPad. 128 gigabytes. I'm early looking forward to filling it will sweet precious music.

Long story short ... I was able to download 160 songs before the new one got to the same state.

Did a wipe, and did manage to get one song downloaded before the problem manifested again.

I really don't understand. I'm ready to return it, cancel my Match subscription, and buy a Samsung. No, just kidding.

Please, someone has to have had this problem. I can't be the only one. Maybe my account is correupted. There is no rational reason that the thing can't download purchased tracks. I could understand, maybe, matched songs failing. Maybe there was something wrong with them. But not purchased songs.

I am almost in tears at this. I'd been looking so looking forward to this problem going away when I got a new iPad.

Oh, it seems to be doing a new trick after my last wipe. The songs download, say processing for a few minutes, and then start downloading all over again. I've watched 4 tracks do this repeatedly while typing.

Help .. someone ... please. You're my only hope.