I've done it, on similar "spend zero dollars" budget.
It's doable.
The controller will not work. It will probably be a TRIAC-based AC chopper circuit. This type of circuit uses the 120 zero-crossings per second of a 60hz AC waveform coming out of a household socket to control the speed.
Basically, every time the sine wave crosses zero, it shuts off power, then delays a certain amount of time before turning on again (the time delay is determined by the "throttle"). So for example, since that pulse will be reset no matter what after 1/120th of a second, if you delay half that time before turning on, it will be at half speed.
These transistors are super simple and super cheap and take advantage of that AC waveform. You'd need some other form of speed control.
I controlled mine with a super ghetto knife switch, and did speed control through the bike gears (ballpark) and slow start (to prevent chain snap) by just ganging up a bunch of scrap power resistors and toggling them into circuit for a few seconds (until they'd smoke) to give the chain a fighting chance.
I didn't ride it much, as I took it apart for final tuning, my family "helped" clean up and took all the custom-cut bolts and threw them into my misc unsorted bolt bin. I kinda gave up and only ever brought it out for demonstration ever again.
https://endless-sphere.com/forums/viewtopic.php?f=28&t=38022 <-- Build thread.
https://youtu.be/sc0HNuTwcBg
The generator... you probably won't have room for, but I'd make a cargo trailer for it. A "bob" style with a single wheel. Then you'll have infinite range.