If you’re not too set on it, I would suggest going with a street board rather than a mountain board, simply because of your cost bracket.
It will be near impossible to hit that, even considering the price of the trampa board alone. My build is a street build, with 83mm clone wheels. I am using some Zippy packs from Hobbyking, and I get around 12 miles of range, depending on what speed and hills and etc.
I can go up any hill I want (I haven’t been conquered yet) and I’ve got a dual 6364 set of TB motors. So I believe you would be perfectly fine with that. I am only 150 lbs, but a few of my other friends who weigh a bit more, have no issues with the power either.
The extra cost for the 6374 motors is gonna hit your budget a little bit too, so I would probably just go with the 6364’s.
I’m in the process of working on a build for one of my friends right now that is close to your price range. Take a look if you’re interested. Full part list: Jalepeno Build
Left off that list at the moment: 12S charger, motor pullies, belts.