Yardburner - The Weber 6501 hose you listed is the same hose I originally asked Weber about using with the Performer. They are adamant that the 6501 hose will not work and shouldn't be used with the Performer.
Their answer doesn't make much sense since the 6501 hose is essentially the same thing as the hose Jules is using, just lesser quality and more expensive. Weber is supposed to follow up with me on Monday and provide a better explanation as to why they don't recommend using an adapter hose with the Performer. If they do provide an answer, I'll add it to this thread.
Also, I ran into a neighbor last night who has a Performer and asked him this same question. He said he went to Lowes and bought a Char Broil extension hose (again, virtually identical to Weber's 6501 hose) and he's had his Performer connected to a 20 lb. tank for about three years now without any problems.