1st timer to this forum, I owned (briefly) a red early 67 GT500 (auto) in the mid 80's. I bought it in the garmet district in LA and had it transported to Phoenix. Don Roberts has told me my ownership history is in the registry for that particular car. Unlike others, I have no interest in owning it again. It was not a rusty POS or totaled out car put back together, it was "just" a used car (CA rust free) at the time, I think I paid $5k for it. The automatic and the heavy nose (big block) seemed to drain any "fun" factor the car might have had, but then I was (and still am) into balance and handling, not straight line ability. My brother-in-law is building a 67 GT500 "tribute" car and enjoys nose heavy big blocks, he has a 428 SCJ 69 Mach 1 too. I do enjoy the small block cars and think that one with late model improvements (alum heads, suspension & STEERING) is the way to really enjoy the car, assuming you actually drive them. The classic design of these cars (even the Mexico coupes) has stood up well and I will likely try to obtain another one (GT350 this time) in time.
These "nose heavy" cars have the same weight distribution as the fox-body Mustangs with 302's. They can be made to handle very good with just front springs and good shocks. I have had mine on many road courses and ran very well. Maybe yours had a worn out suspension and the slush box does not help any either.