Hello,
As far as i know you cant possibly monitor all the tweets.
you can do 180 calls every 15 minutes with rest api. say you want all favorited tweets of the day by 5 PM EST. then at say 3 PM EST. you can monitor 1444 different accounts.
streaming api you can follow 5000 users but you can only monitor 1% of all tweets in given ammount of time and since its RT i dont think you can get any useful information pertaining to favorited.
I can spend a couple hours determining the user lists and it could be dynamic which you can change, maybe you I can pull it from a source.
I can leave the code open so that you can have the code optimized in the future.
Regards,
Steven