OK, I tried it just now. These are the "invalid" modes I allowed getFullscreenModes() to return with my changes:
Mode #0: 5120x3328 - 32 bpp
Mode #1: 5120x3200 - 32 bpp
Mode #2: 4096x2664 - 32 bpp
Mode #3: 4096x2560 - 32 bpp
Mode #4: 3840x2400 - 32 bpp
and if I select any of these with, e.g.
sf::RenderWindow win(modes[0], "Test", sf::Style::Fullscreen);
then it works fine. The "fallback" I mentioned previously must have been because I chose 800x600 in fullscreen initially, rather than one of the fullscreen modes. So ignore that.
Once in any of those modes, if I do a
sf::CircleShape shape(50.f);
then it displays at the same size, regardless of mode selected, which makes me wonder if I'm getting native resolution, no matter which mode I select.