Good question. My first answer would have been to have the shipper specify that your parcels should held at a FedEx location for pickup. The nearest one open on a Sunday is ten minutes' drive from DFW:

FedEx Office Print & Ship Center

However, that would require leaving the airport briefly.

Good question about having something sent to the Grand Hyatt. You might be able to get away with that. I sometimes enter "GUEST ARRIVING [DATE]" as my surname. Then maybe give the front desk person a tip when you collect the package, so they don't ask why you aren't a hotel guest