I'm a team lead

And my boss' boss is tired of hearing that we can't get work done because of the number of calls we get a night.

We are missing two leads out of 6, now our number is 3. There are 5 teams and they're rather large compared to how they used to be (6-8 cells are now 8-10). Our tasks have grown as well (documentation, audits, and sample creation but now we have computerized ticket creation, more audits that take us off the floor all at once, double check of certain lines, and so on so forth).

I didn't stop walking except during my break or when I had to call in to get a ticket printed. No time for the regular tasks. We work from beginning to end, no breathing point after before the next shift (and we are a 2 shift system).

What can I do to improve my time management and get my other tasks done? I can't carry my documents and samples with me to each call. And tonight we had stations down for over 20 minutes waiting. I have asked for help from the bosses but they have no idea. They can't hire more because no one seems qualified.

I just want to know what I can do to complete all my tasks. Do I skip breaks and lunch? Do I let the floor rot in downtime while I do my other tasks? We are so lean that even other departments are struggling.