Well after a hard reset (master reset), the rebooting robot – that automaton of lockups – kept locking up. In fact while driving to work, with the phone sitting on the passenger seat, it rebooted twice. Then once more in my jacket pocket while walking in to the office. I tried to show it to some folks in the office and it locked up and rebooted on them too.
I emailed Verizon customer support back with the news and asked if I could take it to a local outlet to have it replaced. I got some awesome service here and I want to give Kudos to Verizon on this – a rep checked for the closest store, called them and checked availability on the devices, then called me and let me know the address, who she spoke to at the store, and that they had some in stock and currently had quite a line of folks (so expect a little delay). All this from my email note. Well done Verizon.
I went to the store after work and only had to wait a couple of minutes. I now have a new Droid – and I expect this one will work fine.