Thanks for the pictures. I must first ask what is above (on the other side) of the tin you have on the ceiling? How close is that venting (ignoring the metal) to a combustible surface? Like a floor joist? DBL wall reduces clearances to 8-9" but your single wall requires 18" of clearance to a combustible surface.
The owners manual, in four places, encourages the use of double wall stove pipe to help maintain stack temps. I appreciate your observations of wrapping the pipe with insulation. I can't qualify how that is or is not better than dbl wall because I have no data. However, it does appear with that entire chimney located on the exterior wall, cold air is going to be a challenge. That cap is not one that I think (bot an expert on caps) would normally be associated with a wood stove, but rather a wood chimney/fireplace. The liner dropped down inside, you say that it is insulated. Was it a wrap that was applied to the venting on the outside or an insulating material between two layers of metal?
The suggestion to use a torch or weed burner to warm the stack has been used for decades, although not a great solution.