Last night I put up some drapes along the back wall to see what is would do. It made the sound dull.
Complete wall absorption will do that for the high end. Usually you do not treat an entire wall with either absorption or diffusion.
First reflection points, side walls and behind your seating position are also crucial points to treat. But usually require a different type of product than what you would use for bass trapping - i.e. less thickness
Ceilings, like what you have, can also be treated, though with our ML we do not get as much ceiling interaction due to their dispersion properties.
A crazy question. Do bass traps go low in the corner of high?
Both, as bass energy gathers anywhere two walls meet, and gather even more where tri-walls meet.
The best trapping for the corner is floor to ceiling coverage.
If unsure of what to do -
and most of us are in regards to room acoustics, contact Glenn at GIK Acoustics, or Ethan at Real Traps. First decide on which product you want to purchase, GIK or Real Traps, then contact that individual and have a nice discussion about your room. No need to talk to one, and purchase the others product.
BTW, I can really relate to your room, as it is very similar to mine - basement, low ceilings, furnace and HW tank, drop ceiling, concrete everywhere, etc. etc.. My downside is when I moved into the house it was already finished
Dan