Indians, and later voyageurs used a mix of wood ash, spruce resin and lard.
Spruce resin is just collected off of trees. Melt. Once it flows well, filter the sticks and bugs out.
Add wood ash to the point where it is less sticky -- about the same volume as the spruce.
Add a bit of lard to keep it from cracking.
I don't think that spruce per se was requried. Pine, fir or larch probably would work just as well. Note that the the voyageurs carried a pot with them, along with spruce roots and rolls of bark for larger repairs. Birch bark canoes required frequent maintenance. This suggest to me that getting the right consistency to not be brittle in cold water, and not be to soft in hot weather was tricky. Mind you, a canoe has a lot more flexing than a house.
I don't have a recipe off hand. The drier (harder) the pitch is, the more lard you will need. Too little, and it cracks. Too much then on a warm day it flows out of the seam.
For a stationary application like this, I wouldn't worry about the lard.
I would try other fillers too. drywall powder should work. If the cracks are large, try adding a measure of unground wheat bran, or oat husks.
Another alternative is builder's lime. There is a long tradition of lime plasters. While lime is a high energy product, it's not as energy intensive as concrete (by about a factor of 4) Lime/sand plasters take a LOT longer to dry (weeks) but they are slightly flexible -- much more so than concrete.