We'll create fresh WordPress site with Advanced Custom Fields: Multisite Sync installed. You have 20 minutes to test the plugin after that site we'll be deleted.
This plugin does nothing else than to use the internal export function of ACF to filter the data from your main page. After that all fieldgroups of your subpage will be deleted and re-imported. So it’s more of a hack than a real sync.
This has the consequence that the ID integer of your posts shoots pretty in height with frequent use. But that doesn’t really matter I think.