They make some very very thin plexi meant to prevent glare off of pictures in picture frames.
I don't know the thickness, but .05" seems correct (1/20th inch).
I put some on top of the brand new old stock MsPac overlays I bought for my Ms pac cocktail refurbish project, and I like them. I rounded and sanded the edges so nothing to get caught on. I wanted to preserve the integrity of the expensive overlays from bad children/(would-be former) friends

/etc.. and it seemed to work well.
I would not have put on anything thicker like the 1/8" that most stores only have.
I got the 1/20th stuff at Home Depot for about $1.59 I think, but it's small so only is enough for 2 cocktail panels.
I left it on my Bubble Bobble (converted Defender) as it helped keep the stick-on decals from peeling.
Otherwise if you have nomal overlays then I'd suggest no plexi.