Wow, thanks for all the responses, y'all! It's super helpful to hear all these points of view!
The problem is, I see no indication of serious rust elsewhere whatsoever. The previous owner, after removing the vinyl top, has had the car garage kept for the last 15/20 years, (Without attempting to fix the rust!!??) so there hasn't been water pouring in or anything.
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A little rust in there, but surely nothing that would damage the integrity of the car? As for seeing this before I bought it...well, it was definitely my fault. The seller had a patch on it, but I could easily have caught it had I looked more closely.
That is the main worrisome point... But again, the pictures I've posted show literally all the visible rust on the car. Can car killing amounts of rust be hidden under perfectly smooth paint?
That's how it appears to me. Thanks for the encouragement, y'all!
The more I think about it, the more I think you're right about the safety factor. It would be a considerable job to glass it all up "properly" anyway, so I might as well go the welded option.
Selling the car is definitely a distant third for me. It has a pro built 318, and... I kinda love it. I would be willing to learn how to do the repair correctly and/or farm out some of the work to a professional.
Sorry for the long post, and thanks again everyone!