Notre Dame is playing in town that weekend, which is (I think) why in my OP I recommended to book soon. The same is true of the rainy day.Lodging: a quick look shows that lodging around South Bend to be between 2-600 (!?)
Have no idea why other than it is a Holiday (Labor Day) weekend. Have not checked anywhere else.
I would have preferred weekend 2, rather than 1 or 3, of September for this reason — but I can’t due to work travel.
Before setting the date, I did a quick check and there were (hopefully still are) hotels outside of town with better prices.