Is there an economical 2-3 RPM 120v motor with speed control? Or what components could I use to achieve that scenario?
Your synchronous motor for that output RPM is already going to be an assembly with an integrated gear box. A synchronous motor is going to give you a normal constant no load RPM due to the fact that the motor design is based off the AC line frequency. For your variable speed application you will need to source a motor that you can vary the speed of (a small DC permanent magnet brushed motor will be the easiest to work with) and mate that up with a suitable gear box to reduce the speed to the range that you need. 

I would suggest that you do some research into the drive motors and gearing systems used for small wheeled robot type projects. It should be possible to use your mechanical abilities to adapt such components to your application. The robot research will also expose you to the available electronic technologies for controlling the motor speed as well.

There is also a huge base of low cost hardware for motor speed control and components around Aruduino based home built 3D printers. You may want to look into that as well.