Firstly , try and find out if the said artist is actually looking for songs! You do read ,that they can put songs on hold for ages, and then pass on them at a later date, maybe due to changes in music style.
Getting a song in the hands of an A lister is a pretty lofty goal....it would have to be knockout, you do know this?
Twitter is a good potential backdoor way into the real billboard charting artists....but not directly, maybe a songwriter/sound engineer/backing singer etc...they can have the ear of the studio....and i think the 'top' operates in loop of friendships, referrals, lunch dates....you can't get to them ,through personal effort , a publisher(a proper one) with connections to the target artist, might be able to do something..keep trying.