$Cheap$ Motor Speed Controller, 300A

Wow, 300 amps!
I don't think a golf cart motor draws that kind of amps through it's controller.
Since you are talking junk yards, how about a flea market/ yard sale trolling motor, stripped down and geared/belted to the rear wheel. They have a twist controller in the handle and run on 12 volts, much easier to get batteries and parallel them for more AH. Possibly a heat problem, they do run under water and may be engineered to use that for cooling. Of course this would be more in the range of a scooter or moped. Lots of Alternative Energy Vehicle DIY resources on the web.
TomJ