Of course, if you did eventually get yourself a hot air station, QFN packaged components may actually be easier to solder/rework than TQFP (the ones with legs). I've done quite a few in work recently and was surprised how easy they are, compared to how hard I expected them to be.
Maybe see what you can pick up on the cheap, read some tutorials and have a play around? If your board is already broken you're hardly going to make things worse 