moving apps so micro-SD without rooting?

I have a Nabi 2 tablet for my 6yr old. Its running ICS (4.0.4). He loves it and it has been working great. The only problem I am now running into is space for installing additional apps. Its an 8GB tablet so I am now having to take apps off before I install new ones. It has a micro-SD expansion slot as well. Right now, I use this for storing additional videos.

Is there possibly ANY way of either installing or moving current apps from the internal memory to the external micro SD WITHOUT rooting it? I looked into this MONTHS ago and basically was told that Google totally removed this from Android 4.+ & rooting was the only way, but was hoping there is now a solution.

I have seen that this tablet can be rooted & had thought about in order to have Google Play access, external micro-SD access for apps & FULL HDMI output access for certain apps, but have realized that moving apps is now the only thing I am really interested in (Amazon App store and Aptoide have been sufficient for me for getting apps).

Therefore, I would rather find a NO ROOT solution to be able to just move apps if possible. Any help would be great.