For posterity, as of 10:50ish AM:
PC laptop, WiFi: 2 Chrome Incognito windows - both had the same queue ID and got through at the same time, but one was a mess and had no registration links once I signed in; the other worked fine and I got registered.
MacBook, WiFI: 4 private Safari windows, 1 non-private Safari window: all still sitting at more than an hour, though two have bars moving
iPad, WiFi: 1 private, 1 non-private in Safari: both still more than hour, 1 bar moving
iPhone on cellular: 1 private Safari, 1 Chrome Incog: neither budged