I actually tested this for an article I was writing on the .303, with a mate who had a Mauser 96 straight pull. I was using a sportered No.4 Savage. We stood and fired many shots offhand at 50 yards. Both timing for rounds away and hits on the target were to be counted.
In the actual exercise, the straight pull finished slightly earlier by a fraction of a second - basically the same. We didnt bother counting the hits on the target in the end because the Mauser jammed on the last round and we couldnt open the action. Belting it with a rocks turned out to be a bad idea. We later got it open when it had cooled down sufficiently.
I declared the Enfield the winner on reliablity of function.
I have hunted with the .303, and it will give you a follow up shot as quick as any lever action in my opinion.
In my researches I found that the use of the middle finger was never actually taught by the military, although it's possibe some troops may have picked up the idea themselves. I can't really see how it could be any faster than the normal practice.
The deer cullers of New Zealand who contended with enormous herds of deer they had to shoot on foot in the mountains had a technique they called 'fanning the bolt' - this may have been the same thing.
I do know that NZ troops in Malaya would deliberately shoot like this to try and simulate semi auto rifles. This was told to me by vets.
Undoubtadly to my mind the Lee enfield is the fastest bolt action. AS for reloading - damned if I can get the stripper clips to work for me...I always get one rim lined up behind another at least...