I do not recommend reversing the fork. The bike as it is now should require very little effort to balance. (It should feel fairly stable, and need almost no effort from arm muscles, to keep the bike balanced while moving at 10 or 25 miles per hour.) If you reverse the fork, it will probably require effort to balance at 10 miles per hour. At 20 to 25 miles per hour, it might wobble in a way that would cause you to crash.
I do have other ideas to correct the problem you are having.
Like you said, use a fat tire and low pressure (for instance if you use a big apple tire you should be able to get away with 20psi if you weigh 120 pounds or 35psi if you weigh 200 pounds). The minimum depends on the bumps you encounter on your rides -- as long as you always avoid bottoming out your tire (hitting the rim against the ground) you'll be fine.
Other things that might work for you: lean forward when accelerating hard. replace your handlebars and/or change their position so that you are riding more like a bent-forward racing cyclist and less like a beach-cruiser cyclist, since that'll put more weight on the front wheel. Go easy on the throttle whenever moving less than 10 miles per hour. (when starting from a dead stop, don't go past the middle on the throttle)