I know what you're talking about, I've had it too as a kid and try to make it that way for myself. As to the question of when did it change? I think it changed when BBQ became competitive, and over the years the sauces have been made sweeter. What I like, and (what I think you like) probably wouldn't win in competition, and I think that's why it's all but disappeared.
48" Klose Backyard Chef,
Generic Propane Grill, Grey Thermapen, Maverick ET-732