Before I get started, does anyone have fricition drive experience with that 8mm shaft? Need to know if it can hold up. A skirt bearing for friction drive is an excellent idea.
I don't think you understood what Rich was trying to convey. Let's see if I can make it clear from the ground up. The diameter of the motor is 1.985", x pi that'll be 6.184", etc. Two revolutions mean almost 12.4". 30 revolutions is 31 feet. But one (1) volt will spin the motor 270 revolutions in one minute, the surface of the can covers 279 feet. Just over 3.17 miles an hour.
Let's assume you're using a 26" wheel, which I assume Rich meant was supposed to spin 250 rpm. One revolution is 81.68", almost 7 feet. That motor will spin more than 13 times for the wheel to spin once. Rich wants you to go just under 20mph, 776 revolutions being a mile then 1/3rd of that times 60 minutes is 20 miles.
Theoretically if you push that can right on the tire and run 3s, 11.1v, on the lipo, you'll get 3,000 rpm.that's just over 1,500 feet in a minute before you figure on losing something under load. 4s would be over 2,000 feet in a minute, more than 20 miles an hour and almost 40kph.
But this motor is most efficient at 6-8s, over 35mph and over 45mph, respectively. Too fast for just a bicycle.
A nice torque converter with a 2:1 reduction, or just a 1" diameter pinch roller on the end of the shaft, would bring the 8s speed down and make the motor more comfortable going uphill. Probably it would make life easier for your controller.
Specifically for your 24v battery we're taking 6500rpm in significant digits, let's call that 38mph/61kph, you need 3:2 reduction. Maybe a 1.33"/33mm capstan actually touching the tire. A motor that small around, maybe a 3240, will be physically insubstantial and I don't think you want to use such. This motor would only be good idea if the housing is not pressed on the tire, running 4s battery might be risky.
Just one theory.