You need to think about how the force is being applied when you're stringing.
We start with the mains. All the tension is being pulled across one plane. If you tried to string the mains without mounting the racquet, what would happen? The racquet head would distort so that:
a.) it becomes shorter, and
b.) it becomes wider
In a 6-point mounting system, the supports at 6 and 12 are inside the racquet to prevent a.), whilst the arm supports are outside the racquet to prevent b.).
When you mount the racquet, you'll have the supports 'snug' - not tight, not loose. When you string the mains, pressure will build against the supports, so that once they are done the racquet is under the greatest strain. If you were to look at the supports at this point, you'll find them tight rather than snug because of all that force being placed upon them.
As you string the crosses, you're redistributing tension on the frame, to the point that when you finish the racquet head should be the same shape it was when you started. The more crosses you pull, the less pressure is being applied to the mounts. This is why they appear to loosen.
The problems you describe are that:
i.) the supports are 6 and 12 are becoming loose as you string the crosses, and
ii.) the supports on the arms are indenting the frame.
This suggests that the supports at 6 and 12 aren't being tightened quite enough when you mount the frame, resulting in more pressure being placed on the arm supports. This could also happen if your towers are at all loose, so it would be worth checking those.
If you haven't already, check out YULitle's video on mounting a racquet: