I don't know if its an option, but I'll tell you what we did in our '06 Dynasty. Our fan was switched by a round, white rocker action switch by the bed, with a low and high speed function. Our bedroom TV is suspended from the ceiling above the foot of our North-South bed, so 120V power was available near the fan. I drilled into the heat duct above the TV from inside the TV cabinet so I could get to, and use the heat duct as a cable raceway.
We replaced the existing DC fan with a new 120 V AC fan, with blades just short enough that they would not touch either slide, when they were pulled in. I ran the 12 volt wiring back from the ceiling fan to the TV cabinet, and replaced it with 120 V rated cable from the TV cabinet to the new fan.
Then I installed a basic relay in the TV cabinet. The relay coil is rated 15 volts (or so), and the contacts are rated 250 VAC and at least 10 amps.
The fan is no longer a 2 speed fan from the switch, and either up or down on the switch will power the fan. The pull chains and switches on the fan, itself, control speed and rotation.
It has worked well for probably most of 10 years. You may or may not have the availability to get the 110 V and be able to get it work, but it's a thought.
Jim & Angie, Boise, ID
2021 Entegra Esteem 27U
2017 GMC Acadia Denali