What are you shooting that you want the reach of a 400mm-600mm lens? I ask because I recently discovered that my 5D2 will auto focus with my 300mm f4 and the 2x II extender in live view mode. If you're shooting something other than sports or quick moving objects, perhaps a 300 and a 2x extender might work for you. Hope this helps.
So f/8 AF works in live view but not viewfinder?
I unfortunately am known to chase after birds and love shooting them in flight. THAT can get quite expensive in Canon land. I'll try the Kenko 2x TC on the 70-200 MkII, which fortunately has fabulous IS, AF, and MTF to burn, hopefully all enough to compensate for 2x TC effects. It already works great with 1.4x TC..
I have the 70-200 f2.8 IS and the Canon 2x II extender. I have to say that I was quite impressed with both the IQ and the speed of the AF. To be honest when I bought the extender I really was expecting the worst, but ended up being very happy.