I don't know about shooting the 1911, as I don't own one, but I do own a G19. I'm a fairly new shooter, but I find I stray off target if I don't pay attention to what I'm doing.
No matter whether rapid fire / IDPA practice, or slow paper shooting, I shoot the Glock well when I pull the trigger safety back, until the trigger is shorter, then press straight back to fire and resetting only to the short trigger pull, then pressing back again for follow up shots.
In other words, if I pull the trigger straight back from full forward position for first, or follow up shots, my aim suffers, as I have a tendancy to pull or jerk the gun more, typically resulting in a low and/or left shot, whereas if I reset to the short trigger pull, I'm much more steady and subsequently accurate.
I can only assume that setting/resetting the trigger to this point would be more similar to a cocked 1911?
Don't know if that's relevant or helpful, just sharing my limited experience...
Karz