Auto All is fine, but it can't replace Shake and Wiggle since sometimes shaking before wiggling changes the structure quite a bit.
Since I don't really understand what shake and wiggle do, maybe this suggestion won't make sense, but can they have a parameter that specifies how much they do their thing? Maybe this won't work with shake, but I imagine that wiggle might be able to have a parameter so that it wiggles more or less.
I have to amend what I said previously–I just gained a hard-earned 9 points on level 33 using the pull tool. I tried with the drag tool for about half an hour and got nowhere, so I decided to try the pull tool instead, and on the first pull/wiggle, I got 1 point. I got another 8 over the next several minutes. So it appears that using a combination of drag and pull can be helpful.
One of my new strategies is to drag/shake/wiggle until I cannot get any improvement, then pull/shake/wiggle, etc.
Since they are useful separately, we will most likely keep them separate at this point for competition puzzles. However, we think Auto All could be useful in early puzzle levels, to introduce Wiggle and Shake without having to discover the best way to use them separately.