If I understand you correctly, you want to restrict access to that specific servlet acting on the content, but not on the content itself.
ACLs are the natural way to restrict access, and by far the most secure one. Implementing access control on a filter is more work and less secure.
If I understand you correctly, you provide access to this functionality with URLs like this:
/content/mysite/page.myselector.json
If you change that to
/content/mysite/protectedContent.html/content/mysite/page.json
You can add access control to the /content/mysite/protectedContent resource, and then use whatever authentication you like.