I don't see how that room could be anything but WAY too dead in the high frequencies.
What is desirable in any room is a balanced absorbtion scheme to yield an even decay time across the spectrum. The decay time is based on the volumen of the room and what you want to use it for. 2 channel is different than multichannel or HT. Recording is different than monitoring, etc.
You don't necessarily want NO reflective surfaces IMO. Certainly not all reflecting surfaces treated the same - regardless of what's behind it.
Generally, for HT/multichannel usage (where the system generates the surround field/ambient information), you end up with somewhere around 40-50% of the room's surfaces covered. There are some designs where pretty much everything but the ceiling is covered. BUT, those designs have things like batting above ear level, upper bass through mid absorbtion below, bass absorbtion in corners, columns, soffits, risers, etc. In short, a balanced scheme where not every surface absorbs highs.
Those would be the kinds of things I'd hit them with.