I'd have to agree using a router mounted edge guide, either home made or store bought, or you might try laying a piece of masking tape down where the bearing will run. I've used that on laminate I didn't want to scratch, haven't tried it on MDF.
I prefer to use an edge guide anyway, because nothing ruins your day faster than 'tipping' the router and gouging a piece of work.
Maybe a smaller router might help, a laminate trimmer perhaps wouldn't take as much effort to control, might do the trick, just guessing.
lastly, there are square bearing bits, I haven't tried them, but they supposedly don't mar like others do.
http://www.woodworkersworld.net/lami...rim_bits.shtml