It might not be practical for you to brush your teeth on a daily basis.
Maybe once per week is the most that you might be able to comfortably
do.  If you can't brush your teeth well, you might consider other
strategies for allowing you to preserve your teeth without brushing.

You could have a dentist perform a professional cleaning once per
month, and said dentist will also check for any emerging cavities.
You could rinse several times per day with a fluoride rinse, like Act
or Flouriguard.  The fluoride helps prevent tooth decay even if you
don't brush your teeth.
Avoid eating sugary foods or stop any kind of sugar consumption.
Especially, don't eat sugary foods that stick to your teeth after you
eat them, like chocolate chip cookies, oreo cookies, snickers bars,
etc.  Sugar, especially sticky forms of sugar, helps promote plaque
growth and build-up.  The main point of brushing teeth is to get rid of
plaque, so if you have less plaque, there is less harm to not brushing
your teeth.
The big thing is not to allow particles of food to get stuck around
your teeth for any period of time.  So, after every meal, rinse with
water.  Always rinse with at least water after every meal to get rid of
any food particles around your teeth.  Keep rinsing until no more
particles come out.  Examine your teeth in the mirror to see if there
are any more particles.
If you never had food particles linger around your teeth and you never
consumed sugary foods, you could literally not brush your teeth at all
and get few or no cavities, especially if you rinse frequently with
flouride-containing mouthwash.
You could also drink authentic Japanese green tea, 1-2 cups per day,
made from green tea leaves and twigs.  Green tea helps reduce plaque
formation around teeth.

In summary, follow the above advice to reduce plaque formation around
your teeth, and use fluoride and get once per month dentist cleanings
to prevent further cavities.  You should be constantly rinsing your
teeth with water after meals if you cannot brush, and then rinse with
fluoride and not eat or drink anything for about 1/2 hour after rinsing
with fluoride.  The best time to rinse with fluoride rinse is at night,
when you are just sleeping for eight hours.  Plaque grows a lot while
people are sleeping, so the fluoride rinse at night helps counteract
the damage of plaque that develops through the night.  especially don't
go to sleep with particles of food stuck around your teeth.  rinse them
out.

    I'm confused.  Are you saying that you spend 30 seconds per quadrant,
but you feel it would take an hour to do a good job?  Is this an
intention tremor?  I cannot understand why you can shave so quickly but
cannot brush even with a mechanical brush.  Maybe you can elaborate on
what part of the brushing motion seems to evoke the tremor.  Better, it
would help to demonstrate your technique to your dentist, who may well
have some ideas on how to make things less stressful.

Steve