Spotify – Using Spotify Web Player Behind Proxy

Google should help you here
Open Google, type in all the names in this fashion

twttrusr1 or twttrusr2 or hckrboy42

then select option latest from left hand navigation under the more option
You will have a live stream of all your twitter feeds

p.s: do not try to bypass your company's proxy/firewall , it will just jeopardize the security measures taken by them.

No there is no fallback and no alternative other than using trying to use their desktop client.

Spotify is likely trying to protect their music from being downloaded, and this is just one of those methods.

There should be no problem with using WebSockets in your environment.