I didn't try this but I am contemplating to do it:
Curtains are installed on rods and some mounts accept multiple rods. I am thinking on the second rod, behind the one visible in the room, to hang, centered at ear level, some ceiling tiles with high NRC and CAC ratings (like USG Mars). They are light, not messy like fiberglass boards and can be easily hidden behind the the curtains. The good ones are not cheap thou...