I can't believe the freewheel hub hasn't bent or broken an axle yet. I've bent axles on those before and I weigh 140 lbs but I was beating on them pretty hard. As a response to feitsbob who brings up Phil Wood hubs constantly, a Phil hub is probably worth more than the entire bike and would be a huge waste of money in this case.
I'd have the wheel rebuilt with a cheap 7-speed Shimano cassette hub (easily located for <$20 used), 36 double butted spokes, and either re-use the rim or find a heavier one. Have it built by a competent wheel builder and it should hold up just fine.