I would have to respectfully disagree with Larry that replacing gunnels is a big job, or one to be avoided. I have been restoring for almost 30 years now, and I have NEVER spliced a gunnel for fear of replacing them. Personally, I detest the look of a spliced gunnel. Replacing them is, even for someone doing it for the first time, a 1 day job, if that. As with anything, the devil is in the details, and in the planning.
With the canoe you have, I doubt you would have to steambend the new ones. This makes it a simple in/out job. I use a Fein Multimaster to cut off the old nails, cutting into the old gunnel from the top down through the nails. I cut about 1/8 an inch into the gunnel from the rib. The Fein wood/metal blades work great, or the new Imperial titanium coated blades work even better.
Once the nails are cut, the rib will usually part ways from the gunnel with a little persuasion. Then, it is merely a matter of clamping the new gunnel into place using a ton of clamps. (I use the little Bessey "F" clamps, 3" throat. I have about 60 of them, if memory serves) Then, just nail the new gunnel into place using bronze ring-shank nails. Having as many clamps as I do, I usually do both sides at the same time. After that,it is just a matter of getting the new decks fitted and installed, which is even easier if the old ones are in good shape.
***To back up a bit, when I am making new gunnels, I will usually cut out a bit of the old, right in the center. This allows me to get a accurate profile for determining the bevel on the outboard vertical face of the gunnel.***
I would encourage you to NOT splice the gunnels, especially if there are many punky spots. Again, it is, with your canoe, a pretty simple, straight forward job. And, as my father hammered into me as I was growing up, "There is no sense in doing a job, if you are not going to do it right," plus, "Never be afraid of a little hard work!"