It has been proposed that the fourth digit of this SN may have been scratched out, making the real number 2738. This would put it in 1906 and more appropriate with the installation of a motor and the remains of the decal.
This canoe is a genuine mystery. The serial number appears to have five digits as shown below.
The Old Town build record for serial number 27348 shows an 18 foot long canoe with no sponsons so that isn't a good match. The one for number 27378 is from 1913 with sponsons which is a better match for the canoe. However, it has no mention of the long decks shown on this canoe or any provision for an inboard motor. This led to the speculation that the fourth digit might be a mistake that was crossed out making the actual number 2738. This build record is missing which indicates that it shipped before October, 1905. This canoe looks much more like one from the 1905 era than the 1913 era. The information and pictures at the link below show a similar canoe from 1906. Let me know if this doesn't answer your question.
My usual approach to the Old Town serial number records is to start with a serial number from a boat and then go find the build record. Recently I had the reverse experience for the first time, I happened across the build record for serial number 5001 and realized that I had seen some pictures of this one as shown below. It was the first motor boat made by Old Town for Herbert Gray who was the chairman of the board of directors and had the name of his oldest daughter Helen painted on both sides of the bow as shown below. I have no idea where it is now.
I'm sorry for the delay in posting photos. The last two showing the outside were just posted up on Facebook yesterday. I had previously been looking at images from the Antique Boat Museum's pages but those appear to have been removed once it sold. This canoe also looks similar to the one below from the 1905 catalog.