I gave $20 to cellunlocker.net. They said it should take five minutes; it ended up taking about 24 hours, because they said they had to "search additional databases." I'm assuming what that meant was that the phone was so new that it isn't in the standard list of databases out there, and they had to go to HTC.
They emailed me an unlock code. To use it, I put an off-network SIM into the phone (it was locked to T-MO, so I put a Red Pocket (ATT MVNO) SIM into it). It prompted me for the unlock code. I typed in what cellunlocker.net had sent me. It worked. I was able to place and receive calls on the new SIM.