I can't answer why moisture would leak out the seams either, but there should be no moisture in there to leak.......
Any leaks around door or the closed off vent on rear leak air INTO the stove when chimney is warm. Not smoke out. The warm chimney has rising gasses that cause a lower pressure area in flue, pipe, and chimney allowing the higher atmospheric pressure in the house to leak IN. This would allow the fire to burn with intake dampers closed. (that's actually the patented name of them when Bob Fisher's father, Baxter invented them. So your terminology calling them dampers is correct.) Any leaks into chimney or pipe allows cooler indoor air to leak in, cooling the inner flue, causing the condensing issue you have as well.
6 inches above stove is not a good indication of pipe temp. Stove heat will affect the bimetallic spring that senses pipe temperature. Try it at least one pipe section above stove, then compare to the temp of the pipe just before it dumps into chimney. That will show you temperature drop at the top of connector pipe. Double that reading will be the internal gas temp entering chimney. Then you can estimate how much loss you have to the top. Not much with one section of chimney. If you can get a temp reading inside flue near the top, you can correlate 250* at the top to your inside measurements.
Double wall pipe inside will help tremendously.
Split everything but the smallest pieces.
As bholler mentions, rounds simply do not dry. Drying time starts when split, not cut.
Any leaks around door or the closed off vent on rear leak air INTO the stove when chimney is warm. Not smoke out. The warm chimney has rising gasses that cause a lower pressure area in flue, pipe, and chimney allowing the higher atmospheric pressure in the house to leak IN. This would allow the fire to burn with intake dampers closed. (that's actually the patented name of them when Bob Fisher's father, Baxter invented them. So your terminology calling them dampers is correct.) Any leaks into chimney or pipe allows cooler indoor air to leak in, cooling the inner flue, causing the condensing issue you have as well.
6 inches above stove is not a good indication of pipe temp. Stove heat will affect the bimetallic spring that senses pipe temperature. Try it at least one pipe section above stove, then compare to the temp of the pipe just before it dumps into chimney. That will show you temperature drop at the top of connector pipe. Double that reading will be the internal gas temp entering chimney. Then you can estimate how much loss you have to the top. Not much with one section of chimney. If you can get a temp reading inside flue near the top, you can correlate 250* at the top to your inside measurements.
Double wall pipe inside will help tremendously.
Split everything but the smallest pieces.
As bholler mentions, rounds simply do not dry. Drying time starts when split, not cut.