A pair of bungees will hold the tiller near center. A long light line
tied to the tiller, led around the gunnels to the forepeak via blocks
and back again, tied to the other side of the tiller, will give you a
very handy monkey to keep the tiller more or less centre or enable a
correction from anywhere on the boat. Going forward, you can pull the
line along the gunnel fore and aft to pull the tiller one way or the
other. So, you can steer from the foredeck, standing on the tiller line
while you work if needs must. Could also work for a wheel.

I saw this first in a rented motor launch in 1956 in Horseshoe bay. I
was a boy.

A similar setup could handle the gearshift, no?

At sea, you would do best by also having Annie Lectric helm, if only
for dire straights when you really want a backup.

My short bilge keel setup seems to have a mind of it's own, the rudder
is overbalanced in all conditions, she veers as soon as you let go.

Perhaps I should shave the leading edge of the rudder, or stick on a
tail?

Terry K