If you have building security, why don't they just sign for all packages and put them in a storeroom until you claim them? Just like the baggage claim at a hotel, really. You have to check out by noon, flight isn't until late, you leave the bags with the hotel and pick them up when ready to leave.
I do this whenever I go to the west coast: schedule a redeye back east on Saturday night, go eat a nice dinner, pick up the bags around 9-10, head to the airport, enjoy a nice, quiet lounge, and spare myself a night's hotel stay. Catch the connecting flight to my home city and I'm back before noon, plenty of time to unpack and wash clothes before work Monday.