one drill, one suggestion
A lot of our students come with DA/SA guns. We've had good luck with one drill that has already been mentioned.
This is an hour or so of fire, decock, fire, decock. You will quickly get to where your hand is comfortable with its double action SIG or whatever, AND with its single action SIG or whatever, and can switch between the two almost automatically.
You just don't want to do this drill so much that on the street you fall into fire, decock, fire, decock...
One suggestion: historically, auto pistol shooters have actuated their triggers with the tip or the pad of their index finger. It's a technique that goes back to long before the DA auto came on the scene. We found it very useful to learn from the ultimate double action practitioners, the revolver shooters. DA sixgunners most typically find that they get more leverage by contacting the trigger at the distal joint, a spot the old time PPC shooters sometimes called the "power crease."
This gives the finger a great deal more leverage, and in most cases allows a better straight back pull. After the first DA shot breaks, it is not necessary to change finger positions: just leave the finger there at the "power crease" and continue firing.
It works for me, and has worked for a great many of our students.
Another factor (also previously addressed on this useful and thoughtful thread) is trigger reach. A shorter trigger also allows "more finger" and more leverage for, in my experience, a majority of shooters. Ernest Langdon has been mentioned here. I can't help but notice that both the Beretta and the SIG he did for me were equipped with short reach triggers, which tells me that he is on top of this factor, too.
Best wishes. If you try the different finger placement, please let us know how you did with it.