Katie -- you've totally right about the different combos -- Google Play lists 6500 compatible devices, then multiply that by the the firmware variations (often country / carrier specific even for the same phone / tablet model).
I actually have an S4 Mini, but it's the "Black Edition" with LTE and it runs 4.2. Works fine.
Now something a bit more relevant:
The trick on the devices where touching TouchWiz causes it to crash is to not touch it at all.
However, all existing versions of Aqua, when you turn off that setting -- even right after installing -- will send a "0" (none) value to TouchWiz.
Apparently this can be enough to make TouchWiz crash (on some devices).
What I'm going to do is make the app smarter -- so that if you do a fresh install of Aqua, and immediately turn the "launcher counters" setting off, it will know that it's never sent any data to TouchWiz, and so won't be trying to reset the counter to 0, it will just leave it alone.