If you want to keep the nice glass then secondary glaze on the inside.
An extremely cheap solution that will work immediately while you work out something prettier is that heat shrink film you can get from any DIY place - like thick clingfilm, comes with a roll of double-sided tape, get it taut with a hairdryer. What's the finish on the reveal/frame? Gloss is best for the tape to stick, but it'll work okay on other stuff. Get the surface as dry as possible first, so you don't get annoying condensation in between.
If you want to keep the nice glass then secondary glaze on the inside.
An extremely cheap solution that will work immediately while you work out something prettier is that heat shrink film you can get from any DIY place - like thick clingfilm, comes with a roll of double-sided tape, get it taut with a hairdryer. What's the finish on the reveal/frame? Gloss is best for the tape to stick, but it'll work okay on other stuff. Get the surface as dry as possible first, so you don't get annoying condensation in between.