I use double or triple surgeon knots for attaching tippet to leader all the time with great success.
I use loop to loop connection often when I can (fly line to leader or tip, tip to leader, etc) but prefer a direct connection from the leader to tippet.
I believe the berkley vanish is your problem, I have had similar issues and gave up on the spool. Infact, after using a lot of fluorocarbon in various situations, the only thing I really use flouro for anymore is tippet when chironomid fishing. In that scenario I believe its less visibility characteristic and that it doesn't float is an advantage with such small flies being staticly suspended. For just about everything else, I don't think it is much if any of an advantage, considering the cost and finickiness with knots, over mono. In my opinion, when swinging or stripping a fly, as long as your mono leader is appropriately sized, they don't have much time to see it.