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;

http://www.hvi.org/assets/pdfs/CPD/CPDFull.01July08.pdf

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.