Ice dams are caused by poor insulation and/or vapor barrier in the walls
- common in older houses. Warm air gets into the wall cavity and rises up towards the attic. While the top plates (2 x 4 cross pieces)prevent a direct connection enough heat gets up close to the tops of the walls and leaks into the attic at the lowest part of the roof. It melts the snow and causes ice dams. Since there is only a little heat it can only melt snow in the winter warm spells. That's why the dams are worse in warmer winters.
Your high low vent pattern is on the right track - add a few more, especially low ones near the ice dam locations. Naturally snow can block these vents so you may have to take a snow rake to the areas around them. In our city, Winnipeg and very cold, many people use heating wires along the low parts of the roofs to melt ice dams or prevent them from occurring.
The shingles curling is a summer over-heating problem which could also be addressed with more vents strategically placed.
Are the kitchen and bathroom vents through the walls? If so you could add short (just enough to extend past the eave) extensions so the warm air isn't near the roof. Use 90 degree elbows pointed downwards to prevent reverse airflow into the house. The fans have enough power to blow the air out and down.
Your house moisture problem could be solved by addition of an HRV (Heat Recovery Ventilator) to the furnace. These have 2 fans and blow outside air in and inside air out. They recover about 75% to 85% of the heat from the outgoing air and put it into the incoming air. Since outside air is dryer than indoor air they dry out a house nicely. Our house is now too dry if we run the HRV's too much in the winter. The best way to install them is to draw the air from the wet rooms like the bathroom and kitchen. The incoming air can just be routed to the return air duct or any of the other rooms. They come with dehumidistats so you can set the moisture level. Ours can also be set for continous Min, continous Max or 20 minutes of every hour.
HRV's are about 150 cfm - 3 times the flow of a small bathroom fan or the same as a large fan. This is relatively low flow so they run for long periods of time.
You can check out the specs and efficiencies of most HVAC products at this site;
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Section III has the good descriptions of how they work plus all the data for HRV's.
Our house was new construction so we could install ducts from the bathrooms and kitchen but that is too expensive for retrofit. I think HRV's can be installed in attics but I am not sure if that applies to very cold winter areas. Check with a good HVAC company. If they can work in the attic and duct through the ceilings it may work at reasonable cost
- over $1500, maybe $2,000 but that is a wild guess. Units cost around $850 to $1,000 but labor is tough to guess at. Needs electrical wiring, etc. Wouldn't hurt to get a quote.
HRV's can be easily installed in basements near the furnace. Use 2 pipes through walls. This method just gets at the whole house air. Trouble with that method is that you don't get the wettest air from the wet rooms unless you can somehow duct to them. Don't know if it would be adquate to just dry out the house as a unit, might be. If the basement ceiling is open it may be possible to intercept ducts to or from the bathroom to focus on that location.
Another option that should be cheaper is a dehumidifier. If you have space you could put one in the bathroom. The cheapest ones need you to empty the tank manually. The better ones have a small pump but you need to connect the drain tube to the plumbing. Most costly would be a ducted dehumidifier somewhere, perhaps basement. Run a duct through bathroom floor to get the wet air. Best is to route exhaust upstairs somewhere but you could just let it exhaust into basement. That would force basement air with it's odors upstairs. Would dry out basement nicely. Install drain to floor drain or plumbing pipe.