Yeah good idea with the ply wood! the lid or top of the case will have the acrylic screwed in so that should be fine. how ever i will still need to place a support in the middle of the case to also0 help keep its shape better...
This pic should show you what i mean...:
The ply wood will only improve the structural integrity of the base... the view from the top probably wont look as good with the brace i'll have to put in