I have a room with the same width dimensions but only 8’ in height. There are two 48” x 48” panels on the walls covering the first reflection points (one per side) on Z track for adjustability. The listening position starts just past the furthest edge of the panels (from the speaker). On the ceiling in front of the listening position (parallel to the panels edge) there is another 36” x 72” panel basically creating an absorption plane between the front edges of the speakers and the listening position- there is nothing behind the listening position and it is 6’ +/- to the rear wall. It works well.
One question- since you have 10’ ceilings why not adapt the fan base to extend below the thickness of your ceiling panel. Assuming the panel is no more than 2” thick it shouldn’t be a big deal. Create a hole in the panel and remount the fan afterwards. Just an idea-