Amazon Underground APK download location? I am trying to download a game for my child in the Amazon Underground app store.

The problem is, the Underground app refuses to install under my child's login (it claims to be incompatible with my device!?!).  I can install both the Underground app and the particular app I want to install under my login, but I don't allow my child to know my PIN or use my login as I have other things install I don't want her to mess with.

If I could find the APK before it is installed I figured I could just manually install it under my child's login, but I can't find it!  I have run a file manager and did a search under the entire filesystem (as root, no less!) for all files within the last hour, and did not find any APKs.  Some other answers here and here claim it is stored in /sdcard/Android/data/com.amazon.venezia/cache/ or /sdcard/Android/data/com.amazon.venezia/files/apks.  However, both of those directories are empty after the download is finished.  I am looking when it tells me the download is ready to install, but before I allow it to install, so I know the APK must be around there somewhere.  Where is it?
Look in /data/data/com.amazon.mShop.android/files

I had to use Fx to search my entire device to find the Amazon Video APK.