Unvented attic insulation question – GreenBuildingAdvisor

We have a small, two-story wood-framed townhouse in NYC built in the late 1800’s. The top floor ceiling is vaulted to the roof deck in the front half of the house, and there is attic space on the back half that is unvented. Nothing is insulated. The roof is pitched and abuts the adjacent house on one side with an integrated “Yankee gutter” on that side. The surface area of the entire roof is only about 1,000sqft. The attic and air space in the vaulted ceiling room get very hot in the summer. We are about to replace the roof and it seems like a good opportunity to insulate. The current roof has been in place for >20yrs and there are no leaks. 

From what I’ve gathered from reading here and elsewhere, our best (only?) option is to insulate the roof deck externally with rigid foam. I believe we are in zone 4a, and it seems code requires R-33 when insulating entirely above the roof deck.

Problem is, it doesn’t seem that any roofing contractors actually have any experience doing this kind of project. I’m also hesitant to make any major changes to a house that has survived 125yrs without any insulation or venting of the roof/attic

My questions are:

1. Any drawbacks to just replacing the roof shingles and leaving things as is (other than the attic/upper floor being hot in the summer and cold in the winter?

2. Any problem you see with doing external rigid insulation in this setting?

3. How do I find a reputable contractor that actually knows how to do this correctly?

4. How would you detail the foam at the junction where the house is attached to the adjacent building (which is taller than ours), where there is an integrated gutter

Thanks for your input!