Smallest radius roundover bit?

I want to round edges of 3/16" thick baltic birch. This would mean finding a 3/32" radius roundover bit. This will also need a super small bearing OR a thicker pieces to guide it with cut to fit. A guide piece to use over and over is not a problem. But I still need the crazy-small radius.

This is for results that have far too many edges to do by hand (100s of inches per finished product).

Is there any way to devise a table router that could work here? Might require a jig, there might be such a product out there (though I've tried to search), or it might just be impossible.

Chamfering both sides and then milling off the sharp end could work but that's three operations instead of two and wouldn't feel right.