Just to sit and answer my own question (but also trying to contribute to the forum's knowledge!)...
I figured out that if I set interactive: false in the SwipeView, then everything works correctly-- it's just that you can't use your mouse to swipe left and right, which, could be argued, wouldn't be correct behavior in a windows/pointer desktop approach anyway.
I'm guessing that there is something odd that happens in SwipeView when another window is opened. We are planning on targeting a touchscreen/fullscreen version eventually, in which case setting interactive: true and switching the Window creation to Popups would be the right thing to do anyway.
I'm leaving as unsolved for now, just because I'm curious if anyone has any other ideas.