A car transmission is not a suitable propeller redrive, neither for a
car or a boat. Study marine practice carefully: it is the same duty
cycle, and after all, no one puts a Lycoming in a boat even though they
could afford to.

No sensible propeller for 250 hp is going to want to turn 3100 rpm.
The diameter of the prop sets its maximum RPM as the tips must be kept
below Mach 1. Probably, you are going to want about a 2:1 reduction.
With a Gilmer belt drive you need to be at exactly 2:1 or fairly far,
say 1.6:1 or 2.4:1, or it will hunt and skip teeth. With gears you will
want them ideally at prime number tooth counts, such as individual
teeth see each other only rarely, and very definitely not 2:1. This is
what caused the catastrophe known as the Continental Tiara.

Driveshafts are very problematic in aircraft drive applications, plus
which there are substantial negatives to pusher propellers.

You do not want to design a engine package _and_ an airframe. There
are more good airframes than engines, although admittedly many are
better built by factories (one wood design hawked by an arrogant son of
a bitch in Virginia who has never built an airplane himself comes first
and foremost to mind.) Most homebuilts are just not designed for 600+
pound power packages. Most people want smaller airframes, I think, for
lower materials cost and easier garage building, even if they are not
afflicted with the common brain disease pervading experimental
aviation, WSE. (Williamsport Spongiform Encephalitis-a disease where
the brain has cooling fins eroded in its surface, causing the victim to
think that 1939 lawn tractor technology is essential to flight.)