@orthomead I have some experience with ceiling treatments, however, a major/important difference between our rooms is ceiling height. Mine is about 7.5 feet. I wish it was taller.
Important info:
---I have NOT measured my room, aside from my ears and those of a few sharp-eared hifi pals.
---My room is well treated with manufactured (GIK, Primacoutic) and DIY panels and traps.
I built a cloud out of 2" 705 panels, trimmed in aluminum angle stck (L shape). Three 2'x4' panels connected on the long-sides. So, essentially, at first reflection, across much of the ceiling between the speakers. And a forth panel midway, making a kind of "T" cloud.
IMO it worked very well and did not create a dull, over-damped sound.
After about a year, I thought more about the floor, which has a wool/silk area rug, about 4'x8' also in front of and "between" the speakers at first reflection. The underlay pad is good quality and substantial. However, I wondered if I might do better, so I looked for a thick vinyl pad and added it beneath the carpet, in addition to the pad.
I thought it positively changed the sound a bit. So, I wondered if this would allow me to remove the cloud.
In my space, the cloud with a two-inch gap and a two-inch panel, is a substantial visual element.
Removing the cloud was fine. Maybe no net-gain, but no degradation. However (isn't there always a however?), I do think it helps to have good diffusion in a space, so I added two "skyline" diffusors (2x2) at first reflection. I think this is very nice now. I used the compressed styrofoam product from Vicoustic.
Would an even denser material be better? Sure, but ceilings have considerations for weight, mounting, etc.
So, I would ask: Have you considered diffusion at first reflection?
I recognize there are multiple thoughts on this, but I like the diffusion and it helps to keep things lively.
Also, your fan is likely causing some amount of diffusion too. Sorry I don't have better pic of the assembly. This is from the side.