I typed out my initial thoughts before considering a different approach. I think the second approach is better, but I am not deleting the first for your consideration.
Also note there are some asymmetrical radius round over bits, mainly for table edges and are likely too large. The table I am sitting at in Starbucks features that type of edge.
Here are my initial thoughts:
Try experimenting with shimming the baseplate of your router asymmetrically.
I am not entirely convinced that this will work though. And I cannot work out in my head the sequence of cuts. It might be easier to control in router table.
Filament packing tape stands up to abrasion well and had a low coefficient of friction and will slide across the stock easily. Just make sure that the ends of the tape extend past the edges of the router.
One or two thicknesses of tape may be all that is required.
Here is my likely approach to this issue.
I have made draw scraper blades from sections of old hacksaw blades. I ground the profile in the smooth edge of the blade and mounted it between two pieces of wood. I was able to get a reasonable beaded edge to a profile using just that tool. The blade stayed sharp for the entire cabinet door.
There are dozens of videos on YouTube showing how to make the custom card scraper and how to use it. Cutting a profile with a card scraper was surprisingly easy to do (but I did later get a bead edge router bit).
NOTE: I failed to mention that the radius would first be cut with a conventional round over router bit. It would be modified slightly with the card scraper. I would not try to cut the entire radius with a card scraper.
http://www.youtube.com/results?search_query=making+a+wood+%C2%A0card+scraper+blade+from+an+old+handsaw