That's a great story. Welcome to the board.
It's cool you can mount up weedeater motors, but if you get around to making a solid purchase, you can line up a good used mountain bike and a Dax Friction Drive. www.thatsdax.com
It might take some of the engines you can find used, the larger motors with 2 or 3 shoe clutches.
I thought about motorizing bikes since I was a kid, and while they were rare in my experiences growing up, I thought they were very worldly and I wasn't shocked to see one. When I ride mine now, people generally seem surprised by it. It gives me something to do when I'm on limited income and pedal biking just takes too long when I'm tired or carrying things.