Aha! I have solved one of the problems. I wasn't aware that there are two separate auto update schedules that are set independently, one in the main program, and one in the widget. I had only set the one in the main program. I wonder if linking these somehow, even with a message to the user, might be helpful? It wasn't obvious to me, at any rate.

I will see if using the extra call in the script will solve the other problem, as well.