It sounds like what a car with a poorly designed transmission would do. First gear does not have enough reduction to start under adverse conditions. But my wife delivered mail with an assortment of Subaru’s in mountainous terrain in Colorado for years, heavily loaded, steep inclines, and never had any problems…There is a piece of this puzzle that is missing…
Is it possible for a clutch to “fade” in a manner similar to when drum brakes would fade out on a long downhill stretch? I think I experienced a fading clutch on a '67 Mustang V8 when driving stuck in weekend “down the shore” traffic on the Garden State Parkway in NJ. As I recall the clutch was slipping and acting weird. It never acted the same before or after, but this was the worst longest stretch of stop and go driving I ever dealt with in that car.
Perhaps all the hills and clutch slipping in San Francisco had this clutch so overheated that it was fading and slipping. It had enough grab to keep the motor from overreving, but enough slipping to keep foward progress on the steep hills from the normal amount of pull. Once it cooled down it will act normal again.
I think you’re right about the fading. One SF hill after another would do it.