I think this is a technique that is very useful for Klondike. I can't say if it's guaranteed to work - I don't think it is - but I have had quite a bit of success, including the first Grandmaster game I tried (which I completed quite easily, maybe five minutes). It's based on trying to avoid "locking" the stack by starting at the end and working backwards.
1. Without using the stack, move as many cards around as possible, as usual. Continue until no more moves are possible. Do not worry about using "undo", it does not cause problems for the achievement (and is, in fact, necessary).
2. Now click on the stack and, without using any cards, click all the way to the end until the last card is face up.
3a. If the end card can be played, play it and without using another card move to step 4.
3b. If the end card can't be played, click "undo" repeatedly until the face-up card can be used. Use it and without using another card move to step 4.
4. Click the stack until it's back at the beginning, all cards face down.
5. Go back to step 1.
This also helps plan moves a bit or get out of "stuck" scenarios, the undo can be used to go back to a place where playing the card can be avoided or a second card can be played.
Hope it helps!