Indeed, those numbers do make sense, Tom.
Serial # 77808 was issued to an Old Town 25' War Canoe, CS grade with open spruce gunwales and birch decks, thwarts and seats, painted dark green and shipped to Mary A Elcock, Camp Asquam, Meredith, NH, on 20 May 1923.
A second 25' War Canoe with OT serial # 77851, CS grade, open spruce gunwales and 30" birch decks, birch thwarts and seats, also painted dark green, was shipped to the same address that same day.
Looks as if these could be the canoes of your memory.
The scans of these records are attached below-- click on them to get a larger image. These scans and several hundred thousand others were created with substantial grants from the Wooden Canoe Heritage Association (WCHA) and others. A description of the project to preserve these records is available at
http://www.wcha.org/ot_records/ if you want more details. I hope that you and anyone else reading this will join or renew membership in the WCHA so that services like this can continue. See
http://www.wcha.org/wcha/ to learn more about the WCHA and
http://www.wcha.org/join.php to renew.