score:2
Thanks to mkennedy's comment on the question, I found this clock on Ebay and others like it. The key phrase, as mentioned in her comment, is:
silent sweep hand
Combining that key phrase with snooze
led to many options. Unfortunately, I have no way of checking if any of the alarms do not stop beeping after N minutes or X snooze cycles before purchase. If I find such a clock then I'll update this answer and accept it. In the meantime, I hope that this hint helps other travelers with their clocks!