If your problem is shooting on the move, then I would try out the head on the shoulder thing and then you will see that it is even worse than anything else, because as you walk, your body moves a lot, and pinning your head against another body part (arm) will exaggerate the movement to the gun, and your pistol will bob around a lot more.
Shooting on the move is just one of those things that require practice, and if you keep your head up straight and use your arms as shock absorbers when you walk and learn to "time" your steps with you pulling the trigger, then your shooting on the move will improve.
You think I am wrong, then try shooting a rifle at a target 40 yards away while walking toward it, moving laterally, backing up- assuming that the rifle is on your shoulder and your cheek is on the stock- and you will see it is one of the most frustrating things you can do. the barrel is bobbing all over hells half acre.
Try this, safety first. Dry fire while walking forward and backward aiming at whatever target on a wall at shoulder level about 5-10 yards away. While moving and aiming, develop a gait that will allow you to shoot at a certain time during the constant movement where there is the most stability. For me, this is when BOTH feet are on the ground, whether I am moving forward or backward. I am not aware of any method that works fantastic when RUNNING.
I do not say this to fly my own flag, but to illustrate that I am not a hack: I am a master class shooter in SSP in IDPA. And with so many other things, so much of IDPA is just practicing and experimenting with different things and seeing for yourself. If you personally find that locking your head against your arm improves your shooting on the move, then no one can say that your technique doesn't work, because you'd be proof otherwise.
hope this helps.
john l