OK, for other reasons I broke down and rooted my phone, and then eventually figured out how to solve the problem of storing Amazon Prime music on my SD card. It's pretty hairy. The most valuable web page that helped me in this process was here:
ODROID Forum View topic - JB 4.1.2 How to mount ext4 or NTFS
First of all, I believe that it's essentially impossible to do this using SD cards formatted in "FAT" format, which is the standard format. This is because one lacks the ability to set the required Linux permissions on the files which you're trying to place on the SD card. I struggled with this problem a lot before considering other SD formatting options.
I don't know whether this would be much harder with KitKat. I am using a JellyBean ROM on my Motorola Photon Q, CyanogenMod 10.2. I did this because the KitKat ROMs for my phone aren't completely functional (at least the ones I tried), but I think that this problem might be more difficult with KitKat, due to the way it handles SD cards and file permissions.
I think that I could've used symlinks as I originally suggested, but in the end I did something slightly simpler, which was to replace /data/media on the main phone filesystem with a large filesystem on my SD card. It turned out that it was simpler&best to partition my 64GB card into a small 8GB exFAT partition, and a large ext4 filesystem for the remainder of the card. This large filesystem is what I'm mounting as /data/media, and this is where my now voluminous Amazon Prime music resides, along with the ripped music which I own. The small exFAT filesystem makes Android a bit happier about mounting that portion of the card, without feeling upset that it has a card that it can't read. Note that the exFAT partition must be the first of the two partitions.
As a Mac user, I used Paragon's ExtFS tool to partition and format my SD card, although Windows users probably have equally good (or better) tools available.
Paragon ExtFS for Mac OS X - Download Demo
Before I mounted the large filesystem (see the first link above for instructions), I did something like
"mv /data/media /data/media.OLD"
Then after mounting the filesystem, I copied the contents of /data/media.OLD to /data/media, which was now the large partition of my SD card. I was careful to change all the file permissions under /data/media to be owned by the user 'media_rw', as well as having matching Unix group permissions ("chgrp media_rw ...").
I used the instructions in the first link above to use "ROM Toolbox" to automount my SD card correctly upon subsequent phone reboots.
The Amazon Music app wasn't totally happy after all this jostling, so I uninstalled and reinstalled that app prior to performing lots of downloads, and it seems pretty well-behaved now.
One advantage of this filesystem-mounting approach over symlinking, is that the former is "once and done", i.e. I can continue downloading music in the future and shouldn't have to do any more tweaking. If I'd used symlinking, then depending upon the nature of the symlinks I would probably have to build and maintain new symlinks in some fashion.
Please follow up in this thread if you have questions about attempting this, or if you'd like me to post command-by-command instructions, which I'll describe using mostly using "adb shell" or Terminal commands, i.e. the Linux command-line.
