I use the Mr Buddy heater as a back-up heater only in my OFF-ROAD POPUP. This is almost all tent walls and windows so lots of ways to vent the fumes and replace the oxygen..
The Mr Buddy says they are safe to use if used correctly but I do not feel safe using them. I used them all the when I was tent camp camping.
With an enclosed trailer like you have I most definitely would not feel safe using them.
I feel your pain on the propane furnace. My furnace is WAY to hot to use in my POPUP trailer. Runs us out with too much heat. Can't seem to adjust it. It is also WAY TO LOUD to sleep with. We just warm up the trailer good before getting under the covers and leave the furnace set for 40 degrees or so.
Installing one of the CAT vented heaters would be the way to go.
Check these to photos out... No worries using these heater.

Of course there is another way that some are playing with being using your hot water as a source of heat.

Been some good results doing something like this as well..
Roy Ken