I agree with what has been said above. After I started getting forwards, I thought I was at a point to start sending out material to libraries. I did some research, found a couple I thought would be a good fit and sent a cold email. I got rejection emails in return. BTW, I don't think you should contact a forward - wait for them to contact you.
Later, when I was contacted via a Taxi relationship, I sent that same track in for consideration, and they signed it. I don't know what changed, or who listened to it the first time vs. the second - but it has a lot to do with building relationships. This is a relationship business at the core.
My advice is to write a lot, listen to a lot of what's on TV now, read the listings carefully and write, submit, forget. That is what ultimately worked for me (that and networking with fellow Taxi members here on the Forum and at the Rally). I am now signed with 6 music libraries and starting to get placements. And it only took 3.5 years!

cheers -
kc