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Doing it by hand with sandpaper is a nonstarter.
Also I don't have a lathe :-/
I'd probably chuck them into the drill press and take a rasp to them. You could get it consistent by using a consistent technique, and checking them against a gauge (e.g. cut a profile in a piece of cardboard).
I'm fairly new at the whole woodworking gig, but I think what I would do is create a negative of the round that you want out of a different piece of wood and then jam some sandpaper into that negative and connect it to my drill.
I've actually tried this! The problem is that the sandpaper is too thick to bend neatly in that tight a radius. Maybe I could buy raw grit and stick it in the cavity with spray adhesive....
You don't want the whole hemispherical cup. Just a semi circle.
The best and traditional tool for the job is a rasp. I recommend a Shinto rasp. Surprisingly fast and easy to use.