As I said before, I've never considered my swiss guns to be fast, but just now I got down a k31 and a savage mod 10 short action bolt gun and compared them for speed.
The swiss is way faster than the savage. Don't have an Enfield handy and have never fired one so can't comment on it.
Some observations: I can keep the swiss gun on my shoulder and slap the bolt back with the palm and the base of the little finger on my right hand. The hand very quickly wraps around to the other side of the bolt and is easily and quickly slapped forward. The butt of the rifle never leaves the shoulder! At the rearmost of the bolt pull the cocking ring just barely touches my nose (it's a longish one
) Recovery and return to sight picture is much faster thant with the savage bolt.
The savage was palmed but the need to push the bolt upward and then back made recovering the sight picture slower than the swiss. I could keep the short action savage on my shoulder also. Palming the savage was slower than operating the bolt with the thumb and forefinger mainly because it kept the whole rifle more stable in the hands without the upward and sideward push and twist that happened when palming.
The other thing about palming was that it requires that the right hand and arm be lifted higher than when operating with thumb and forefingers.
I got out an Mosin m38 too and gave it a try. As with the savage, it was much faster when operated with the thumb and forefingers than when palmed. My hand goes much faster to the wrist and trigger of the fun after operating with the thumb and forefingers than when palming on both the savage and mosin.
Regarding the Mosin, I saw some actual wwII trench footage of a russian soldier fireing his 91/30 and he was holding it to his right shoulder and coming across with his left hand and operating the bolt that way. After trying it, I concluded that the guy was either left handed or wounded because it is NOT a good way to operate the mosin. Mainly because the bolt comes back and hits your right hand or more specifically the thumb on your right hand while you grip the rifle at the wrist.
None of the three rifles required taking the butt from the shoulder to operate and therefore would not need any push pull action on the rifle itself in order to fully operate the bolt. I have heard of this method of moving the rifle itself out and back as the bolt is operated but it seemed to be a technique for hunting dangerous game and maybe was done out of necessity with magnum actions??
A looser and smoother bolt action than the Savage could be faster when palmed but I've got no Enfields to test and have never fired one.