If you think that motor is a poor choice - how about you suggest one???
That last line is genius, he's just quoting a point on the diagram, speaking of which this motor is less than an inch in diameter, and with the optional gearbox at a stage in reduction that could be useful to your needed rpm at the crank it will generate so little power you should not be able to feel it unless you are picking the bike up off the ground to use the motor.
https://www.vivax-assist.com/en/product/vivax-assist/vivax-assist_4-0.php
This is essentially what you are trying to create, a hidden motor that powers your bike a bit. Notice this is 200 watts, that's decent for something 31mm in diameter, but it's also something you could actually feel, I'd say probably something like 50 watts could be felt but only minorly. This is also something around 24 volts by the maths, which is a decent step up from 12.
I would suggest a motor if I had a clear idea where to look for something suitable, electric motors are just a world of needs and ability to be made cheaply enough, so something perfect might not even exist, often these things are built to demand, not like engines that are endlessly copied (but similarly you'd be hard pressed to find certain arrangements in specific sizes or formats, especially as they get more complex.)
What size seat tube do you have, that would be a place to start before anything since that's our limit, what is the inner diameter of the bottom bracket as that will affect motor rpm due to limits in availability of gear sizes? A one way clutch is cheap and easy to acquire, and can be small enough for something like this.