Okay, this is based on no experiments at all, so I can't back up this opinion. I think that the tension in the mains does rise when stinging the crosses, for the same reason that crosses end up lower. The reason is how I think the relative strength of the oval behaves.
If you would take an unmounted automobile tire and compress it, it would behave the same no matter if 12 o'clock was facing up or turned to 9 o'clock. Picture an oval, rather than a round and even make it a more extreme oval, like length 1.5 times the width. If you would try to compress that oval with 12 pointed to 9 o'clock, it would compress much more easily than if 12 were straight up.
So we string mains, and our machines are designed to resist 12-6 compression, on top of the inherent resistance the shape offers. When we string the crosses, the sides compress to some degree, increasing the tension on the mains that existed before. (although they are of course simultaneously losing tension as time passes!!
) And as additional crosses are put in, the additional compression reduces tension on previously strung crosses.
I am not going to get into the fact that this would mean the crosses' tension would be higher at the bottom than at the top, strung top down. Because I just want to dodge that issue entirely!
That's my story, and I'm stickin' to it!