Acrylic does expand quite a bit due to heat, obviously, the thinner you go the more any heat affects it. I dont really see it as being too much of an issue though.You can get 1.2mm acrylic and if you give me the spacing behind the sheet and the backbox front, ill have some rectangular clear cut for you to use as spacers - these simply glue into place. You could then insert the clear sheet in the backbox in the BG channel and then insert the BG... if we get our spacing correct then the BG will simply clamp it in place... whole thing holds itself in position.
or - you could simply tape it in place along the BG trim.. wouldnt notice it at all.

...all food for thought!