Guys, it really isn't that bad.
Rheostats are
so last century.

More to the point, they are horribly inefficient. Use a PWM controller, so, "Yes", you need one of those pulse width modulated controllers. In the same vein, you use the electric motors to brake and reverse, which is trivial, plus you get all of that energy back. Good news is that the controllers are widely available for car conversions. (I was amazed when my electric car buddy showed me
his home brew design for his race car; it was a one million watt controller, but if you do the math, that would be what you need. A PT is just slightly ahead of golf cart power, way behind cars. And yes, Virginia, the controller is totally water proof and sealed. Ditto the motors, but I don't think that they are submersible in the normal configuration. With a little engineering, anything is possible.
As MR brings up, you will need to have a computer controlled differential, or wire the motors diagonally, but, again, the commercial car controllers do allow for it. You will need a new steering controller. (If you raid it off of a Prius, you would get some snazzy on wheel controls.)
Seriously, it might be a step above grandpa's shade tree engineering, but not much. There are lots of sites devoted to electric conversion.
There are even members amongst us with race records for electric vehicles... (No, not me.)
And no from an efficiency perspective, you don't want to have a hydraulically driven tractor power by an electric pump, although it might be the low cost solution and the easiest to implement. If you aren't religious about it, it is by far the simplest. The motor could easily be activated and governed by the hydraulic pressure in the various circuits. This is definitely something grandpa could do.
All the best,
Peter
The PT uses four hydraulic motors, one at each corner, in a series/parallel configuration. As you all know, standing still, if you turn the steering wheel right, the front right wheel rolls backwards while the rear right wheel rolls forwards. While that is going on, the left front wheel is rolling forwards while the left rear wheel is rolling backwards. How are you going to replace the hydraulic motors with electric motors and achieve that same motion and not spend a gazillion dollars doing it? It would require some very expensive controls.