Motorola has put a few tools onto the Moto E to help conserve storage and to offload stuff to the SD.
You're already aware of the first one, which is that Moto has reinstated the "Move to SD" option for apps that support it. Just keep in mind that only a chunk of the app (sometimes large, oftentimes small) is moved. The main part of the app must reside within the internal storage. There are more comprehensive options, but those do in fact require root access. These solutions vary from moving entire apps over (even if the app doesn't support moving to SD), to actually swapping your MicroSD and internal storage so that the phone thinks that your larger MicroSD is actually the internal storage.
Another option that Motorola has included is the ability to move media to the MicroSD from the phone's internal storage. It seems you're already doing this manually by saving your media to the MicroSD. But just to double check, go into your settings --> storage, and select media (photos/videos/etc.) If there's anything on the internal storage, it should give you a move to SD option.
Lastly, Motorola allows you to change the save location in the stock camera. Open your camera and ensure that you're saving your photos/videos to MicroSD.
Beyond that, outside of root, there is very little that you can do. The Moto E is technically a smartphone, but it was meant more for emerging markets and for those migrating from feature phones. So you're going to be very limited in what you can do. For your next smartphone, if your needs are more higher end, try to go with a slightly better device for this purpose. The Moto G LTE, for example, supports all the same "Move to SD" options as the Moto E, but has 8GB of internal storage. Or you can get a slightly cheaper Moto G sans MicroSD and LTE, but with 16GB of internal storage. Lastly, their top model (Moto X) comes in 16/32/64GB internal configurations (no MicroSD).
I hope this helps somewhat, and I apologize if this isn't what you wanted to hear.
