I'm afraid that I don't completely understand what it is that you describe as a "problem".
You say that the cutter head seemed short, but short by what standard? Do you mean that you think that the case had to be inserted too far into the collet?
If so, the further in it goes, the better (short of not being able to grasp the case enough to pull it back out when done), because you want it to be in as much as practical in order to maintain the alignment of the case to the cutter. That is, the further in the case goes, the more surface area of the case being controlled and held by the collet. That's the best way to maintain a straight alignment into the cutting assembly.
You then mention using a spring to bring out the cutter head, and it seems to me that would keep the cutter from being rock solid snug to the shaft which in turn would promote variation in case cut length. The cutter is the most solidly in place when it is screwed all the way into the shaft.
It sounds to me that you wouldn't keep getting a "+" variation on your cut if you would have just a little more patience and hold the case in another half second in order to allow the cutter to do it's work. When properly adjusted, you would get your most dependable case to case length of cut by making SURE that the case is allowed to come to rest on the Shoulder Bushing, and stay there a fraction of a second longer in order to let the cutter finish cutting while the case shoulder is actually resting solidly on the beveled surface of the Shoulder Bushing.
The way to think of it is to imagine holding the case in for a full minute or even a half hour (of course, that would be silly). If you were to do that, the case would achieve it's perfect cut every time because it would cut to the shortest adjusted cut length and not be allowed to cut one bit more no matter how long you held the case in because the Shoulder Bushing is what provides the rock solid rest (stop) for the case.
On the other hand, if you pull the case out a fraction of a second before you give the cutter a chance to do it's minimally adjusted cut, you would routinely get a "+" measurement because you didn't let the cutter finish it's job.
So I'm not really sure what "problem" it is that you are having other than not letting the trimmer work the way it was designed to do.
And as I said and as you yourself sort of complained about, you do NOT need to worry about nor try to stop that initial wobble. It's that wobble, and then the subsequent settling down where the wobble is completely gone, that you know when the cut is complete.
In other words, don't fight the wobble, use it to your advantage as a perfect indicator of when the cut is done by the wobble completely disappearing.
Embrace the wobble. ;)
That's the reason why I spent so much time explaining exactly WHY you get the wobble, and what it MEANS when the wobble disappears.
You see the wobble as a problem while I see it as a very nice feature for what it provides as an indicator of a finished cut (by it's disappearance).