Look here, You need an Inshave.
http://www.leevalley.com/wood/page.a...at=1,130,43332

I bet that would work nicely to clean-up with after routing using a jig.

I am guessing it would be difficult (for me) to stay consistent from chair
to chair using that alone.

Thank you. I might need to get one of those suckers!

I have also seen it done with a jig and a router and you can also buy
preformed seats.