Gakkou Gurashi failed the "you have five minutes to make me care about any of this" test initially for us; a friend later convinced us to watch the first episode all the way to the end - they were absolutely correct and it is now firmly back on our to-watch-more-of list, but haven't got round to confirming it stays good yet, good to have corroboration.

Another honourable mention: Akagami no Shirayukihime; strong, actually intelligent female protagonist in a misogynistic fantasy setting. Straight romance. It's a little self-aware initially - she tears up in surprise a bit too often when men aren't actively horrible to her - but gets better. Not as strong as Akatsuki no Yona though, would really like to see a second season of that.