Kershner states that the maximum thrust force occurs when the plane is
standing still (at a fixed throttle setting, I guess), and decreases as you
go faster.

There are some fast homebuilts for which this won't be true.
They have fixed-pitch props with very high pitches, and the blade is
largely stalled at the start of the takeoff roll, making accelleration
dismal indeed. The pilots report that the airplane seems to come alive
at some point before liftoff when the prop blades finally get to work.
My own Jodel has an efficient wooden prop and I often note a small RPM
drop as the airplane accellerates through about 20 MPH. There's
something happening with the airflow through the blades, probably to do
with unstalling, or, perhaps (less likely) with leaving behind the
larger prop vortex generated in the static condition.

Dan