My boards are solid under the bed. I used the 24-inch carpet squares to go down between the board and the mattress. That helped alot for keeping cold air from getting thru.
I too would not like to mess with air mattress. Air mattress will rise and fall with air pressure between day and and night. The colder the night gets the more pressure required. I suspect you would be constantly putting in air...
We use the carpet squares, then the standard mattress, then a 3-inch memory foam topper. The MEMORY foam has strange properties of its own as they will get hard as a rock when approaching freezing temperatures.
We always have a good air flow inside the POPUP when in use. The only way we found to stop condensation was to stop breathing which of course is not a good option. Moving the air around with our O2COOL 10-inch AC/DC/D-CELL fans from WALMART/LOWES did the trick for us. Not fun being woke in the morning with water dripping on your nose from the metal hoop supports...
All part of living with thin solid walls mixed with plastic windows and fabric tops.
We do what we can with the situation at hand and our idea is to have fun times no matter what.
Roy Ken