Is it possible to register an options page and then put the link in to the default Appearance area of the admin?
Or if not there, have the link appear below the main admin appearance button?
Both are possible, you just need to specify the correct parent
Below appearance set the parent = themes.php
or you can use my add-on plugin that lets you add options pages through an admin interface: https://github.com/Hube2/acf-options-page-adder
I’m currently looking for feedback on a new version that also duplicates field groups for use on multiple options pages: https://github.com/Hube2/acf-options-page-adder/tree/Fieldset-Duplicator