I eventually used 1/4" toggle bolts through the innermost siding (with longer bolts than came with the toggles) where I didn't hit wood under the bracket, and construction lags where I did. The highest bracket has both sides in solid wood, so that's good, the middle both toggles, and the lower near a window one of each. The pole is 2' in the ground so secure on that end.
An idea I thought about, but decided against, was to use short lengths of the shallow Unistrut/Superstrut across studs, then mount the brackets to that with the square washers as a base for the bracket. That would have allowed sliding the brackets left to right for alignment. But I couldn't find studs that deep even with a good stud finder. Still, maybe this idea would be useful to someone else.