Only a couple of things to add.
Winni, you stated that you have two gable end vents and a ridge vent, but no mention of soffit vent. If you in fact have venting in your soffits, you need to remove the two gable end vents, they are disrupting the airflow in the attic. Gable vents are an inefficient form of creating cross ventilation and I say that only because most are completely undersized to create enough air flow to satisfy demand for removal. Soffit vents and roof vents work together to allow a proper flow of hot air escaping the roof and not creating warm air pockets that melt the snow on the roof. If you do not have soffit vents then you have what you have, it would not be cost effective to have someone install them.
You also mentioned that you have six inches of insulation on the attic floor. Is this blown in (loose, wool looking) or fiberglass batt. And are you sure there is only one layer.
The reason I ask is loose insulation and fiberglass batt at a thickness of 6" is only R-19 of insulating value. NH PUC Code on current residential construction is R-38, that is 12" of standard fiberglass or loose fill and just under 7" of high density foam.
If it was my house and this was an issue that I had, I would have foam insulation installed in the rafter bays and eliminate the insulation on the attic floor. The foam gives far supperior insulating values and does not require ventilation between the insulation and the roof. You will also get at a minimum of a 10 year warranty on this product and it will never change in R-value as loose and fiberglass will.
As far as installing Bitumen on your roof, one it sounds like you only have an issue with the bay window, so deal with that unless the roof is in terrible shape on the rest of the house.
Installing Bitumen on the entire sub-surface of a roof is commonly known in the trade as protecting against a poor installation. Most roofing manufacturers will not honor their warranties on the shingles if they have been installed over nothing but Bitumen. They main reason is that the Ice and Water shield heats up more than Tri-flex 30 or felt paper (not much felt being used these days but you still see it from time to time), this causes the shingles to breakdown prematurely. Industry standard for installation of Bitumen is 6 feet off the eaves and 3 feet out of the valleys, it will also typically be installed in areas of complex roof line meetings or up cheek walls on dormers (with standard step flashing above to protect the membrane.
(I am not trying to say anyone else did a bad thing by having Ice and Water installed over the entire roof, but these are a few things that you may not have been made aware of at the time.)
As far as shoveling off a roof to clear an ice dam, there is one important thing to know when it comes to ice dams. Ice dams form when melted snow or ice runs down the roof and comes in contact with freezing cold air. If you rake off the bottom 4 feet of snow, the ice dam will move up the roof 4 feet. If you are going to clear the snow off your roof, do the whole thing, it will be easier in the long run (having to do it all winter) as the ice pockets will be slim to none. If you are not interested in climbing on the roof to do this than ask and family member or neighbor that is. Good hot soup throughout the winter is allows a fine payment in my book as long as things are held in this capacity, don't try to pay a contractor with a bowl of soup if you have to hire someone.
The possible main cause for the issue with your bay window is a lack of insulation within the bay roof itself (unless the bay roof is an extention of the main roof above), contact an experienced finish carpenter as this can be remedied from the inside, but make sure they are aware of what you are looking for and know how to properly insulate the space, there is no ventilation in a bay window roof, so you will want them to install a 2 in foam board layer directly touching the roof sheathing, then LOOSELY pack fiberglass insulation into the remaining cavity. If fiberglass insulation is crushed below the thickness stated for the R-value then it will loose its insulating quality. Just like wearing layers of clothing, you will be warmer by wearing loose fitting layers than wearing 6 shirts under a jacket.
Make sure that the leak issue is resolved first, it is always easier to determine the source of a roof leak from below the roof than above. Roof repairs can be perfomed in the winter so this is an issue that can be resolved before spring.
Good luck with resolving your issue.
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