From my limited experience, it is difficult to get a perfectly matched router bit for a given profile. If you are willing to compromise with a close match, then I wonder whether you could make something good enough with a multi-bead router bit? You can find double- and triple-bead router bits from several sources.
Maybe cut one side, flip the board, align it and cut the other side?
Extend the bit (risky) do one "set" of beads, then raise the bit and do the remaining beads, something like that?