In my comment form, how do I move the “notify me of follow-up comments” box above the “post comment” button?

Are you sure nothing get happens with some JS code when “Notify me” button is checked?

This option says :

If this option is enable the subscription box will be above the submit
button in your comment form. Use this when your theme is outdated and
using the incorrect WordPress Hooks and the checkbox is not displayed.

I suggest to you to check the call of your comments template and if an update is available for your theme.

Good luck.