Why don't you try first to filter by notifications?... notifications allows you to add parameters like since. For example (using Facebook pages):
https://graph.facebook.com/PAGEID?fields=notifications.since(2015-3-31 00:00:00).limit(250).include_read(true)&{id,created_time,updated_time,unread,object,link}&access_token=ACCESSTOKEN
Once you got the json data, loop through data, get the ID and send a second request but this time using the PAGEID_POSTID edge. Something like this:
https://graph.facebook.com/PAGEID_POSTID/comments?fields=id,from{name,id},message,can_remove,created_time&limit=1000
Voahla!... there's no need to read every comment!...
Note 1: A Page access token is required, along with the manage_pages permission
Note 2: Use the parameter/field include_read to get all the notifications, even the already readed
Note 3: In the second request, use the parameter/field "filter=stream" to order the posts and get the comments made in the name of your page
Note 4: Don't forget to control the asynchronicity once you loop!
Note 5: Notifications duplicate posts, use an array to avoid to read more than one time the postUse the parameter/field include_read to get all the notifications, even the already readed