In Android 6.0 ("Marshmallow") and later memory management for "external" SD cards has changed a little. One option when first formatting the external memory is to use it as "adopted memory", which basically treats it as a permanent storage unit. However, since certain Android resources really absolutely should not be stored on something that MIGHT get removed (even if the user has sworn that they won't), the removeable SD card is still treated as a logically separate unit from a storage perspective, but many apps, like Apple Music, won't recognize it as removable storage. In this formatting mode, you can install (most of) your apps on the integrated external memory, too--assuming the memory is fast enough. So, this is why, even though you have an external SD card installed, the option to download to it isn't there. However, you still need to change a setting, or all your downloads will get saved to your internal memory, eventually (as happened with me), filling it up and making the phone near inoperable and impossible to install any new apps, etc.
What you can (and should) do is set the app to store all its goodies on the external SD card instead of internal storage. You won't be able to easily remove the card and plug it in somewhere else to access the music you're downloading to it, but you already made that choice when you formatted the card. You can do this either in the Storage & USB settings or in the app settings. If you've been accidentally saving all your music to the internal storage, in Storage & USB, select the Internal memory and then select Apps. It'll give a list of all your apps and the storage they're hogging, in order of biggest to smallest. Select Apple Music and tell it to change the storage to the removable card. If you have a lot of music already stored, it will take a few minutes to migrate. There's also a setting in Settings>Apps>Apple Music called "Storaged". Clicking on it will tell you what storage unit on your phone is bing used, and a button to CHANGE it if you want.
I hope this helps anyone else with the same issue/question.
