Sounds like you've had all those body resto. nightmares rolled into one. We definitely know that design tended to encourage some of the rust. The vinyl only complicates the problem --holding the water in. And yes, inheriting a poor and improper restoration is perhaps the biggest nightmare. A few years ago, I had a guy from a major restoration shop in SC tell me, "For every minute it takes to paint a car, you need to spend thirty prepping it."
Right now, my 68 is a mutt driver. Eventually, when I do fully restore it, I will probably put the vinyl on it. The original color is butternut yellow and a black vinyl top really sets yellow (and several other colors) off. Having said that, I've literally talked with dozens of people at shows and meetings about vinyl tops. There are lots of war stories about rust, bubbling and cracking, (Of course, that's true with or without vinyl.) about liking or not liking the look (So far, this poll proves that a vast majority like the look --at least on the right car), and about originality. (I must confess my trim tag is YY, and that's the one point where I'm seriously considering not going original in the restoration.)
With or without the vinyl and even as a driver, I try not to drive when the road is wet, let alone when it is raining. When I wash the car, about an hour after drying it, I go back with a blower (low speed) and dry out the underbody and all the seams. If anyone wonders about rust, they ought to try that. A lot of water does sit under the vinyl trim, etc.
Thanks to everybody for their input!