Success!
My own test results arrived this morning, just as I was getting ready to cancel my flights to leave tomorrow instead. I'm on the plane now.
I had to leave the house around 6:15 am and the test result arrived at 5:31 am. I was sitting in front of my computer and did some other things before calling the airline. I was in the process of dialing when the e-mail came.
The Vault site has some explanation why different samples take different amount of time to process. Sometimes results are inconclusive and the sample needs to be tested again, sometimes they can't get a good result, etc.
All in all, Vault did come through. First result was received a little over 9 hours after UPS delivered the samples, and the second result took a little over 20 hours.
The samples were shipped to Piscataway, NJ.