I appreciate the responses, and will look into your suggestions. I suspect that most of it is beyond me, but it's good to know that at least in theory a PID controller can produce the same result. However, it seems that applying the PID method to any other system (a different hotplate, or a toaster oven) with different lag characteristics would require retuning the PID, which might actually be more complicated than trial-and-error changes to the manual sequence.
One thing I remember from one of the toaster oven controller kits is that it requires you to do a "learn" trial first, during which I think it turns on max power to 100C, then shuts down and watches what happens after that to see where and when the temperature maxes out. Apparently it then adjusts the PID factors accordingly. That's pretty fancy if it works. Automatic tuning.
But there's one big advantage to the manual sequence method, and that is that the operator doesn't have to be responsible for placing the thermocouple properly every time he reflows a board, which I suspect is a major cause of fried boards. In working with the manual sequence, I've found that thermocouple placements is a bit trickier than I thought it would be. But once a manual sequence has been determined and tested, after that there is no feedback, and no need for the thermocouple, and every time you run it, it produces the same temperature profile.