Doing a bit digging in the message logs, it seems that each message is tagged with its location.
(000000):s8ge:[T]{042A04DA} | The mallard seems alert.
(3C5A98):s8ge:[:]{042A04DA} | You go on shore.
(000000):s8ge:[T]{042A04DA} | The mallard seems alert.
This allowed me to narrow down the map square of the punt. It turned out to be within an inland lake.
Somehow, moving over the zoomed out map allows your punt to sail over a land bridge. However, when in the zoomed-in mode, the land bridge will be present.
This is not intuitive when you're following the shoreline to look for a place where you "last went on shore". In this case, following the shoreline will never get you to that location.