Not sure where you're located but there's no reason a 4mm x 100 mm shaft should take that long. Here's what you should get. I ordered a pack of these a while ago and they work fine with a 30A esc motor combo.

The ESC specified for yours is only 10 A so your shaft doesn't need to be super strong or precise.

The transmitter/receiver should work fine together, I don't have first-hand experience with either one but according to their specs, you have more than enough. The power for the reciever will be routed through the ESC from your batteries.

Good luck!