Is the ceiling finished or open beam?

The ceilings are all finished.
I should add that because of all the skylights and dormers, adding insulation to the top of the roof is not an option.

It is not clear how you intend to access the rafter cavity for any of the solutions.

If you insulate the roof with a permit, the building code will force you to vent the rafter cavities and that will probably require vents top and bottom at the vaulted ceilings.

The absence of venting will not reduce the life of the asphalt shingles although some roofing manufacturers still pretend that is the case.

In this installation the purpose of venting is to allow moisture to escape from the insulated rafter cavity rather than to cool the roof. Ventilation with exhaust fans is rarely effective or energy efficient. You should avoid a negative pressure in the roof assembly.

The heat retained by the roofing material is mostly dependent on its color. Light colored asphalt shingles might be cooler than the wood shingles. But adding insulation is the most effective way to lower the heat gain from the roof.

The term "breathing" applied to the envelope of a house means it is vapor permeable so moisture is less likely to be trapped in a cavity and possibly condense against the colder sheathing. The traditional solution is to install a vapor retarder on the warm side of the insulation but to know if it is needed in this case would require more information.

Spray foam insulation might solve all of your problems if you can get it in the cavity. This is a difficult design issue so don't expect a good solution to be cheap.

If I understand your roof construction correctly, using a ridge vent and soffit vents is a stock solution that probably does not make any sense. It works well with an open attic with trusses because convection draws air in through soffits at the bottom into the open attic, and exhausts it at the ridge vent. However, with your roof style I am not sure how the roofer would connect these two points so that convection would work. Even if there is a way to open a path for air flow at top and bottom, any insulation in the celling cavity would block the movement of air.

Bruce

The soffit & ridge vent combination would send air up through the space between the plywood deck and the batting tucked between the rafters and out the continuous vent on the roof. Each skylight and dormer would of course obviate any flow. Given the limited value of the venting, what do I need to do to reduce the risk of moisture?

Renovator8 - the rafter cavities would be accessed when the shakes are removed, probably also by removing some of the furring strips. It will be a tedious job, which is why I have most confidence in roofer #1 and #3, who are prepared to be flexible. Incidentally, is it crazy to do this in the winter? Will my heat loss wipe out any discount??

When your house was constructed there may not have been a specific venting requirement for the roof style and may now not be.

Depending upon the rafter run you may have more than a single row of bridge/span blocking, which may effectively also block air movement.

Additionally the skylight framing can also effect air movement.

Shake are usually installed over spaced sheating and asphalt over solid sheating.

I'd almost bet that the "condition" of the third option may result in a building dept. determination that results in the least costly option is rigid insulation and reframing the skylights.

To advise you we need to know the permitted occupancy of the building and the construction of the roof.

What is the roof sheathing? Will the rafter cavity be open when you are replacing the roofing? Will new sheathing be installed?

In some northeast communities an open wall or roof cavity in an occupied residential structure must be filled with insulation. If the structure or occupancy is altered the insulation might have to meet the building code for new construction.

I don't know enough about this building to tell you what to do but from what you have told us I'm not confident that any of your contractors has a good understanding of the issues involved. Personally, I would not ask a roofer to design any aspect of a house even the flashing. No offense intended to roofers but they don't usually have a lot of experience designing houses. The absence of a house designer is probably why you have come here but we need to know more about the project to be able to help you.

Many very educated and experienced people have very different opinions about "hot" vs. "cold" roofs. You've got a lot of reading to do.

I think that old wood roofs were installed over a sub roof with big gaps between the boards. This was for ventilation. So your roofers may be able to insulate from above once the shakes are off. I dint know a lot about that but there should be venting above the insulation. And plan on the expense of totally covering the roof with plywood otherwise they will be nailing to nothing in many places and your new roof could blow off. And yes there are contractors who would do this even tho they should know better.
Kathy

In a cathedral roof a vent cavity would be created between the insulation and the roof sheeting with baffles made for that purpose. Installing them from above might require removing all of the furring strips. What would be the purpose of keeping some of them anyway? You seem to be hanging on to parts of the old roof that apparently prevent you from building an efficient code compliant roofing system.

Quality of workmanship tends to decline when its cold outside.