What a horrible situation! I' m always apply as far in advance as I can, after a co-worker just went through something like this. She applied during the holiday season and had a visa sent via one of those courier companies. It was sent out and was supposed to arrive overnight but took almost a week; it got mis-directed and due a combination of holiday volume, a Canada Post strike and weather it took a week to get to her. She still made her flight. Total failure on the part of the courier company. She couldn't even speak with customer service as the phone lines started rejecting calls and it took a week for an email to be returned. However, not all of us are in a position where we can apply far in advance so I' m not judging anybody who applies close to departure.

In this case it' s worse and was totally mis-handled by UPS. They could have done more. If I was the OP I would sue UPS for any damages caused by what was clearly their mistake. Making companies pay big time for their screw-ups will make them less likely to lose things in the future.