upstairs rooms that have walls that are shared with attic space are always difficult to condition. hot in summer...but in winter heat from downstairs makes it easier to heat. in my experience it is the walls themselves that are the cuplrit...not lack of hvac. attic temps are extreme. in the summer the attic temps can pass 130 degrees. R-13 batts in walls just doesn't stop the heat transfer. you can throw more money in hvac at the area...but it will be at a preminum cost, both in equipment and costs to operate. fixing the walls is a one time cost. then conditioning the space is achievable. walls shared with attic should be insulated. usually batts stapled in place, in full contact with wall, and no gaps or voids. then a foil faced foam sheathing board, nailed to the faces of the studs. foil faces into attic space to reflect heat out of walls. install is with button cap or roofing nails. sheathing is caulked to studs, top and bottom plates & all seams are taped. this install both insulates and air seals these problem walls. do a site search of FROGs family room over garage...to see that these are common problems with rooms that share attic space. southface inst has great detail in their air sealing pdf linked below...page 5 http://www.southface.org/default-interior/Documents/airsealingkeypoints.pdf best of luck.

I know of no building code in the US that recognizes "equivalent" R value for a reflective radiant barrier (other than the R value for the air space) although the barrier will definitely lower your energy costs. Maybe there is a performance trade-off you haven't told us about or a code amendment for your jurisdiction. I would have expected the designer and/or builder to have anticipated providing space for the code required insulation before starting the foundations. Why are insulating companies proposing R 20 if the code requires R38? What R value was shown on the building permit drawings? Your entire post is a conundrum. Even with no venting and closed cell spray foam you will need at least 2x6 roof framing which looks to be the case although it would be helpful if you told us the space available. I suspect there is something important you haven't told us about this project. For instance, if you are using the Prescriptive compliance method and if the roof insulation is full height over the exterior wall top plate, the R38 requirement can be reduced to R30. Is that the case? This reduction does not apply to the U-Factor, Total UA Alternatives or Performance compliance methods. Another way to reduce the Rvalue requirement is to use software that allows tradeoffs between different parts of the envelope. Any of these insulation design methods must be calculated and recorded and approved in the building permit documents. You should not be discussing the required roof R value with contractors.

I try to avoid terms like "true" or "pure" and prefer "historic" instead. Often the name people use to describe houses comes from real estate listings. Realtors use a shorthand or lowest-common-denominator to simplify the issue and encourage as many responses as possible. The styles are generally Colonial, Victorian, Craftsman, Ranch, Cape, Contemporary, etc. My 1891 house was featured in the 1892 Architects and Builders Supplement to Scientific American magazine as an example of the new "Colonial Revival" style but it was advertised for sale in 1983 as a "Victorian". One of the most common house styles in America is rarely identified in realtor listings. There's nothing wrong with the realtor approach for their marketing purposes but when discussing the design of your own home with interested homeowners and design professionals, it greatly improves the discussion if you are more specific. A quick study of historic Capes might help you. A house style that evolved over hundreds of years can be an incredible resource whether you intend to make it historic or not. When I visit the Cape I take hundreds of photos. The houses are spectacular. For instance, the front facade is often taller so the cornice is higher than the second floor like this modern Cape in VT. The transom light above the door is one of the most characteristic features of a Cape. But these old houses were framed wth a version of post and beams with continuous wall framing so raising the cornice in a modern version can be more expensive. Here are some interesting Cape photos: historic Bow roof in Chatham

Are the hexagonal windows for light or just air flow? I feel like updating them to something rectangular would be a greater return on investment than painting such nice neutral brick! I’d also look at ways to make the entrance more special, more substantial railings, instead of two small light fixtures one bigger fixture, move the address number somewhere more visible. I think the flower boxes are quaint, but I’d get bigger shutters, ideally shutters should be the size of half the window and your house facade totally allows for proper sized ones!