At least FedEx was taking it to the leasing office for you...Looking back at your OP, you say "One of the big 2 shipping companies..."
MY experience with FedEx, is them leaving $1200 worth of computer parts on my apartment doorstep, shipped from NewEgg. With NewEgg, any purchase over a certain amount using PayPal requires a signature. So, not only did the tard leave $1200 package on my door, he then lied, and said he dropped it off at the leasing office, and forged my signature, saying that I signed for it....at the leasing office....why would I sign for a package, at the leasing office? Hell, I would have been happy if he would have left it at the office, it's better than it just sitting at my door for 6 hours, with a giant NewEgg label on the box, for anyone who knows what NewEgg is to swipe.
I almost claimed theft to teach the lying SOB a lesson, but I have a conscious, and couldn't bring myself to lie and steal for principle.
The best of luck to the OP and quick recovery of the missing package.