The issue with non-fan rated boxes is the screw attachment between the fan and the box. Fan rated boxes have more threads than just the 2 or three threads through the sheetmetal.
The "right" way to do this is to open the drywall enough to install the right box and patch when you're done. The patch can be pretty small and you can probably find some sort of trim to hide it.
One "not so right" way to fix it is to make sure the box is firmly supported to the framing, put in a couple of extra screws if you can figure out where the framing is. And then install your fan mounting screws with a couple of back up nuts inside the box to prevent the screws from pulling out. A drop of lock-tite to prevent them from coming loose and you have something that is at least better than you have now. And without spending the thousands on UL testing, I still think I could come up with something that's stronger than boxes listed for the purpose.
Now, I'm going to get slammed for suggesting option 2. And I believe in following the code whenever practical. But I also think the code only is one way to do things safely. Fire away.