Well, I changed the time to 20 seconds and the next time I tested it, I didn't get the ding immediately as I accepted the quest. So either changing it to 20 seconds fixed the problem, OR it is as you said, sometimes the quote event registers before the quest log update event. In any case, I listed it as a "known issue" and have posted the first beta of the mod here:
Escort Event Alert
Thanks again for all the help and input!