It turns out that there were two issues at play here: rounding errors
meant that pixmaps were almost never the same size as pagePainter
thought the tiles should be, and the tile-is-the-size-it-should-be code
path was broken (but only hit in rare cases, seemingly at random).
To help with rounding errors in the future, I added a geometryF function
to NormalizedRect that returns a QRectF. In general,
device-independent-pixel points/rects should be floating point, and
device-pixel rects should be integer.