You can take your time raising your arm, only your following swing must be fast and of course your “allowance” in front of the object greater than at slower moving objects.
As you get proficient, increase the distance you stand from your target and increase its speed.
It is a mistake to have a small target for practising. When you miss you cannot see if you have missed behind or in front, and you get to dwelling on your aim.
As to the distance to aim in front, that is a matter of experience and, other things being equal, the man who has this experience can beat another shot who can hold closer on a stationary object, but does not know how far to aim in front of a moving one, or how to swing and time.
The difference between shooting at an upright man moving and an animal is that, in the former case, the most important thing is to judge the proper distance to aim in front; in the latter case, to keep one’s elevation so as not to miss over or under.
When shooting at a running man target, the man being narrow, one is very apt to miss just behind the back.
At a running deer one cannot, if at all a decent shot, miss him behind his tail (though one may miss past his chest in trying to shoot forward enough), but it is easy to miss over his withers, or under his brisket.
Keep on practising at moving objects, varying the distance and speed constantly, and the direction from right to left and left to right, till you can judge how far in front you must shoot for each case.
It is best to always use the same pistol and charge. If you use at one time a .22 pistol and then the .44 duelling pistol, you will get confused, as the .22 goes up much faster and consequently needs less allowance in front of the target.
As long as you keep to the same pistol, you need not mind how slowly the bullet goes up. You know how much to aim in front but, if at one time you must aim an inch in front and next time four inches for the same speed, you can never learn to judge where to aim.