I determined that it's easy to do this, with one complication.
My plan is to add the hack to ubb_edit_post.cgi/sub perforum_edit(). The date and time of the original post are available in $post_info[3] and $post_info[4]. The format of those values is determined by the date/time settings in the control panel (that's the complication).
I haven't decided whether to write the hack for a single format, or make it general enough to handle any selected format. I'm also not sure whether changing the control panel date/time format setting would require a cache-clear, to avoid confusing the hack.
In any case, I would convert $post_info[3] and $post_info[4] to the format YYYY-MM-DD-HH-MM (year-month-day-hour-minute), get the current date/time less 15 minutes in that same format, and then do a simple string compare to determine whether to suppress the "edited by" annotation.