I am the same way. Standing in one spot absolutely kills me. On most of my cruises (Magic/Wonder) we arrive early and can sit on the boxes that they have around the promenade deck (we always speak to the Assembly leader to let them know it is a mobility issue, not a laziness issue). If we do that, they do allow us to sit through the drill - but know there will be people lined up in front of you. They also give us the option to leave a few minutes early but we find that just gives us enough time to be in the middle of the next assembly station crowd where you are then standing in crowds trying to get through to stairs or elevator that are hopelessly crowded. So we just wait out the crowds because we aren't in a rush.
Now on our recent Fantasy cruise, we could not sit on the few boxes they have around the Promenade deck because they use them to pile up the cushions from the deck chairs. We were standing still for 1/2 hour on the first cruise and I was in pain for the remainder of the night and the whole next day because of it. I tried to find a solution on the second cruise (we were back to back) but the Assembly leader just said they could let us go a couple minutes early. I was able to lean against the back wall and that helped a little (I was just in pain the rest of that day, not into the next day), we were standing for about 20 minutes. Next time I may check with Guest Services for a wheelchair to use during the drill. I know I'll get looks from people but they don't really understand that standing still can cause tremendous pain.