If there absolutely has to be a line skip, give everyone three and be done with it. No more adding new ones during the day, jockeying for drops, hovering over the phone, etc. Just three and out. Or two, if that's all the system can handle. Yes, some people would have an advantage at getting the big ticket ones.
Yes, I know it's pointless to speculate, "it is what it is" etc. This could feasibly placate a lot of people and ease pressure on the system. But it wouldn't make money short term, so it's out.