The root of the word Ya'amod means to stand in place. See Hebrew dictionary here. Thus why do we call up someone to an Aliya with the word Ya'amod? We are not asking him to stay in place, we are asking him to come up to the Bimah? Is it not more proper to say Yavo יבא or Yailaich ילך or Ya'aleh יעלה or some other word that means to go up to the bimah rather than a word that means to stand in place?
I suspect the reason we say ya'amod rather than yavo or one of your other suggestions is because we are stating the important part of what the oleh will be doing: standing before the Torah. Sure, you've got to walk up there in most cases but that's not the important thing. Plus, what if the guy is already standing up there? He wouldn't have to do any walking at all.
It means that the person is being called to stand in front of the Torah and to have the aliyah. The point is that the person is being called to stand before the king. Since the hinr of the calling is the standing during the aliyah, then the language used refers to that.