Music Composers Unite!
It used to be free to join PRS as long as you had at least 3 published works but now anyone can join for a small fee.
After that either 1) your publisher registers the work or 2) if the work is unpublished, you do it yourself online at their site.
The PRS administers royalties relating to performance and broadcast and it requires the user of your music to send to them a cue sheet of whatever music they use.
If the track you have in a library is exclusive to the company then they will administer any mechanical royalties ( sync rights, etc) and they will register the work with whatever society they belong to.
For unpublished works, if you know of definite performances, live or broadcast, you can notify the PRS when you register the work.
I doubt you will get any significant money for downloads and the rates for Sky are pretty low but you should keep track of every broadcast you know about and make sure you eventually get something. Again, it relies on someone at Sky sending in a cue sheet with the title of the work and the composer/s and the duration of use. PRS will pay your share (100% if unpublished and written by yourself) according to what the rate per minute is for the particular usage.
I hope that helps.
I'm curious to know what it is it about the GEMA system that you consider outdated?
I can't really add more to the answers to your questions but could add that I believe under reciprocal arrangements between societies (internationally) they deduct 10% before passing on the royalty collected to the other society and that process might take a couple of years (from what I've learnt about how SACEM works).