Twitter update with media using wp_remote_post

My question is simple, but the internet doesn’t seem to have an answer so far. Basically I need to send to twitter a statuses/update_with_media request, but I must use the wp_remote_post function to do so. This is because we are using VIP servers and using cURL is not an option. For more details you can visit my other posts, any help is greatly appreciated.

https://github.com/Automattic/wp-codebird/issues/6
https://stackoverflow.com/questions/20133371/updating-twitter-status-with-media-using-wp-remote-post