I assume you have the old board to use for a pattern of the cross section.

I know that white oak would be difficult to shape by hand plane or any of
the power tools you mention.

For my 3" thick plywood rudder, I use a 4" disk grinder fitted with a
special wood carving wheel. This is a steel disk with chain saw teeth on
it's edge. Very aggressive cutting, so go slow and careful..

The PacNW wood carvers use these along with their regular chainsaw tip to
carve detailed statues.

Just rough out your board shape and finish with the plane or belt sander.


--
My experience and opinion, FWIW
--
Steve
s/v Good Intentions