Condensation Dripping

[PA Mountain Man]

The situation as I understand it from your posts and pictures. Clear water dripping at gap around pipe and ceiling trim plate and also from the lower edge of the trim plate. The finish on the wood ceiling appears to be water damaged at the lower edge of the trim plate. You have never had a fire in the stove. The dripping does not occur during heavy downpours. The dripping starts when the T-stat is set at 70 and I'm assuming that's at a height of 5'. From your picture on the roof after removing snow around the stovepipe there is water on the flashing cone, but not on the flue pipe after removing the snow. Your picture of the stove pipe above the roof with undisturbed snow appears to show melting of the snow around the flasing cone. There is a ridge vent on the roof and I assume some form of venting at the soffit. This would lead me to assume there is an air gap below the roof deck and above the insulation if ceiling is insulated with fibreglass batt insulation.

Based on this information, I would bet on condensation forming on the outside of the stovepipe and the inside of the flashing cone above the trim plate and below the flashing cone.
The flashing is not a typical detail I would use, but it is possible to make shingles over flashing watertight using iceshield and sealants. Since the drips do not occur during heavy downpours, I would rule out flashing issues for now.
Condensation occurs when warm and moist air comes in contact with a surface that is cold enough to allow the water vapor to change state to liquid water. Your flashing cone and stove pipe provides the cold surface inside the roof structure.
When you warm up the cabin to 70 at 5' above the floor the temperature of the air up at the ceiling at the trim plate is much higher, maybe over 80 degrees. This warm air will transfer heat to the stovepipe rapidly. Also gaps between the stovepipe and the trim pipe will allow warm air to flow into the joist cavity and if the area around the stovepipe in the joist cavity is open to the roof vent , the warm air is going to flow and keep bringing moist air into contact with the cold flashing cone. I think that may be the reason the snow is melted away from the flashing cone.
Another contributing factor as mentioned above is unvented gas heating. This introduces moisture into the air when gas is burned for heat. A humidifier could also be increasing the humidity level.

Solution #1
Remove the ceiling trim plate.
Seal the underside of the roof deck tight to the stove pipe with an approved material based on the type of stovepipe.
Insulate the entire void in the joist cavity around the stove pipe with an approved material based on the type of stovepipe and provide a channel for air flow from the soffit to the roof vent that does not contact the stovepipe.
Seal the ceiling to the stove pipe, again with an approve material.
Reinstall the ceiling trim plate.

Solution #2
Take me fishing for a week.

 

[Hogwildz]

Now when we are not there it is set to 50 with no issues. At 70 we get the dripping.

That there, tells me it's condensation.
Using the stove should remedy that, although you may get some condensation when first starting the stove.
Are those planks the roof decking also, or is there insulation on top of them.

 

[Hogwildz]

Yeah, that last shot looks wrong. The flashing should be on top of the shingles on the bottom. The way they did it any moisture coming off the flashing cone is going to flow under the shingles.

How to Install a Flashing

How to Install a Flashing - Our step by step video and guide will ensure that you properly install your DuraVent roof flashing with out any leaks. - NorthlineExpress.com

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May not be the case, but some roofers install that last run of shingle as a "cap" piece over the bottom for asthetics. It's ususally laid in roof cement. Does'nt necessarily mean the installation is incorrect. Won't know till some removal and investigation.

 

[Hogwildz]

Some recommendations, consider as you wish:
Take the bottom "square" trim piece off, and see exactly what is behind it? Decking, then insulation? Just decking, paper & roof flashing? Warm pipe through cold spot with no insulation as a buffer = condensation. The higher you raise the interior temps (from other source then stove) the more condensation will occur. As in your experience of the 50 = dry, 70 = wet.
My money is on this as your issue.
If this is the issue, I personally would take the underside trim off, get some fire rated spray foam insulation or Rockwool, and insulate the area around the pipe in the inside cone of the roof flashing where pipe runs through, to create a break point to stop the heated air from rising and traveling up the pipe. It would also stop condensation inside the flashing.
Maybe start with the rockwool first to see it it helps, and then spray foam if results are good.

In some instances, the gap between the outer roof flashing & the pipe, although covered with the storm collar (ring), if the snow gets up to that height or higher, and the gap is not sealed, the higher indoor temps can melt the snow while warmer air rising through the gap, letting snow run in gap & down pipe sides to the square trim cover, and drip drip. Water always find the path of least resistance.
Is it still dripping after you rake the snow away from round the pipe & flashing?
Doubt this is you issue.

It could be damning, but I doubt it in your case. Damning needs much freeze/ thaw to build up under shingles on that steep a pitch. It the dripping happening as soon after the place heats up, or over the course of a few days? Damning usually is a slow progression till it builds up enough to leak. And needs several rounds of thaw/ freeze. Most diverters behind stacks are to protect the stack from a heavy snow load sliding down and tearing the piping off. Usually out in western US and on metal roofs. Still not a bad idea in that area due to snow loads there.
Doubt this is you issue.

Also in rare occurrences, I have seen roof ridge vents, usually the cheaper metal ones that are just nailed over a strip cut out of the decking at the peak, leak. I had it happen here, and have since replaced with shingles over venting. Water can come in a the ridge and run down undetected till it hits an opening or low spot, then enter. In this case it would be the area of decking cut out were the pipe runs through.
Doubt this is you issue.

If there is no insulation at all between the decking & shingles, that is a problem. Heat is rising up & out unchecked, with only tar paper & shingles to contain it, which they slow it, but ain't containing it.

That's my 2 cents, consider at your own discretion.

If you're not using the stove, remove the pipe through the roof, fill in the deck spot, and shingle over. Problem solved.
Or, burn the beauty while you're there and problem solved.