If it's just mechanically loose, you could try and get lockwashers under the mounting nuts inside the chassis. Try something like a locking hemostat to hold the necessary parts in place - it's gonna be quite a tight fit, and desoldering all wires connected to  the socket for easier access to the mounting hardware would be a monumental pain in the rectifier.

When socket pins are loose, you can sometimes gently pry tension back with dental pick. (turn the amp off, and let if fully discharge for half an hour or so before pulling all the tubes from their sockets)

If however, you've decided to replace the socket altogether, you might want to hire a local oral surgeon who dabbles in tube audio as a hobby  :D  -  like I said in the first paragraph, there's not a lot of elbow room in there.   Parts Connexion has a very interesting new production octal socket based on an old Western Electric spec that might be interesting, particularly the 3 claw contacts.   If bakelite was good enough for WE mil-spec, it's probably OK for audio.



http://www.partsconnexion.com/catalog/tubesockets_files/image082.jpg