What type of ebike motor would work best for a 13” tire?

Good afternoon,

Whilst I appreciate you prefer to use bicycle parts, you may find it beneficial to search for scooter or wheelbarrow hub motor/wheel. The benefits of which would be - they're water tight, they're simple (a nut to hold the axle at either side is all you need to secure it) and they have lots of tread.

You can also run it using a motor controller which has a "walk assist mode" - this will disable the throttle and lock/limit the speed to around 6km/h, alternatively as previously discussed - physically impede a thumb throttle to limit input.

A 36v "hoverboard" battery would be fine (and small), all the torque is at the bottom end of these motors so that's not something you should worry about.

If you're looking to run more than one motor simultaneously - that's not something I have ever successfully accomplished, it is possible you can just disassemble a hoverboard - use the footplate pressure sensors to turn the motor controller on when you grab the handles, the gyroscopes as the throttle - so the cart accelerates when you lift the handle(s), each of the wheels to drive one side of the cart.

** In fact, don't do any of that, I think just invented something!

All of these things exist, regrettably I am unsure of the rules in relation to posting links but if you're still looking, let me know.