Marc,
Sounds like you are already on the right track! A few questions to help refine the answer (which many others can give you as well) and then I will make some generic suggestions. But first lets get to your questions! Or skip to the end for the suggestions!
1) What to control the motors with. See below!
2) Rheostat or potentiometer. These are doable. Rather old school, not very efficient or easy to use, and will get very hot. But if everything else sounds too confusing, yes heavy duty rheostat that goes from 0 to 5-10 ohms and can dissipate at least 75 watts.
3) Using Something like an Arduino. You KNOW that with this group, that will be the first think we will suggest! :) Yes, an Arduino could do that with some bells and whistles added. Se below for suggestions.
4) A normal load, whether it is a light or a motor or a toaster will try to draw the current in proportion to voltage. So really controling one is controlling the other. Yes, at 9V the motors will turn slower and with less torque. But if you use a PWM controller that is fast enough to make the motor turn smoothly, it will seem as if the motor was being driven by 9 V instead of 12V. If you have to have the full torque, then you have to slow down the PWM until the mtor jerks forward with full torque and speed for the fast bits and then suddenly comes nearly to a stop with no torque during the PWM off cycles if you want slower than full speed. But I am sure you don't want jerky motion, so that means living with the 'apparent' lower voltage in.
The first and most important, do you require the motor spin at 'exactly' 2 rpm? Do you want a dial with detents or digital keypad and display to get precise speeds? Or do you want a continuously variable input to adjust to what ever speed 'feels right' at the moment? Such as maybe having a foot switch like the one for the TIG?
Do you want to run in either direction at the flip of a switch? Do you want to go forwards and backwards during a single weld by slowing down so much it starts going in the other direction?
A) Real simple, one direction only, steal the speed controller from a battery powered drill/driver! I am guessing that the 18V lithium drill drivers are strong enough to handle you set motors as long as you are not sitting in them :) . And if the lithium ion drill/drivers are too well made to get a working motor driver out of, the cheap harbor fright motors usually have a very simple trigger pull pot to small heat sink packed electronics and then to one wire of the motor. Jut cut it of and stick it between the battery and one wire of your turn table.
B) An Arduino to run a PWM signal through a MOSFET "H" bridge motor driver would give you forward and reverse at the flip of a switch, or as a continuous of a knob with forwards full speed at one end, backwards full speed at the other, and zero somewhere in the middle. It can also tell you what power level you are putting out. If you want to pay extra for optical encoders it can tell you the precise speed. You can even use a coarse speed adjust knob on the box and a fine adjust on the foot pedal speed control!
C) Almost as old school is using a 555 timer. You only need one PWM signal, and you can probably live with yanking over a big double pole, double throw switch to change direction. So just a lowly 555 timer, and potentiometer knob on the box or in a foot switch, and a single MOSFET or IGBT to pulse the power and you would be set. No programing, just experimenting with capacitor and resistor values to get the range of speeds you want. But NO bells or whistles!
D) If you really do need an exact, precise, digital speed, you are going to need optical encoders to measure speeds that slow. Assuming once again a case of 2.0 rpm is desired, that is 30 seconds between ticks of a tachometer. But an optical encoder disk with a mere 250 lines gives 1000 transitions per revolution, or about 33 pulses per second, and much higher resolution disks are available so that you can get very precise, smooth, constant rotation at 2 rpm if that was what you wanted. This would almost certainly need the arduino to convert the pules timing intervals into a speed and then change the PWM to adjust to fit. And the optical encoders are a bit pricey unless you can get a left over on from a FRC robotics team. And they have to be VERY well taken care of or they scratch or warp or move out of focus.
Ok,questions hopefully better understood, and suggestions ranging from cannibalize a HF drill/driver to working with an Arduino person to make a disco version of a potters wheel!
Hope this helps!
Mike