In the Graph API, which is the "permission to install custom tab"?
According to the change log, this is a 90 day breaking change, https://developers.facebook.com/docs/graph-api/changelog/version2.11/#gapi-90-pages
/page/tabs— Creating custom tabs with POST operations will only be available to Pages with 2000 or more fans, or pages managed by whitelisted apps. Existing custom tabs will be unaffected.
90 days in relation to the release of API v2.11, which was on November 7, 2017 - so you're starting to see the effects now.
This sounds as though the page tab add dialog was not affected (at least to me, I have not checked yet) - so presenting your app users with the dialog could allow them to easily install the app on their pages themselves, maybe give that a go. You can call it either via the JS SDK's FB.ui, or by redirecting the user to
As CBroe suggests, installing a page tab using the redirect method still works.
Edit: sadly they've closed this loophole too