A 3/8" wide tenon is pretty small to use a bearing guided bit to round over. I would use my Dremel set up as a router. W/a 1/16" round over bit that has a brass pilot bearing.
Or you could cut the rail tenons short and make some plugs to fill the hole and let extend proud of the legs. I have done this by taking a short 1X6 and cutting a tenon across the end and rounding over the edges and cutting the tenon into plugs to cap the rails, this makes them all end grain and the same look to the grain.
Just a suggestion,
Herb