Sounds like a tough call. The idea of routing in multiple passes
sounds good. Another idea is to find a router bit with a larger
diameter (bit diameter, not the radius of the cut profile). For
example, a shaper bit has less tear-out because the cutting edge isn't
pulling away from the wood as much due to the "flatter" path it
follows (much larger radius of travel).
If you do a lot of these, you might want to set up a second router in
a table or hung under a piece of wood, with a bit the next size
smaller, to pre-cut the edges. For example, for a 1/4" radius, the
pre-cut could be 3/16".
Also, if the bit isn't sharp, replace it. Buy carbide, not HSS. Bits
don't last forever.