Is it designated "storage" and above a garage? That means that the floor joists will need to be re-engineered for a live load, as well as the entire roof needing to be re-engineered. Insulating such a space properly isn't cheap either. Nor is adding the right sized ductwork and zone for the heating. Probably have to upsize both the furnace and AC and air handler. Then there's actually finishing the space out with the drywall, paint, carpet and proper windows that can serve as an emergency exit in case of a fire. It would probably cost more than that after the fact to pop the top over the garage and re-engineer all of the above down to road after you close.

I solved my room over a garage problem early this year for right about $550 just blowing dense pack cellulose in the 5x20 ft kneewall, sidewalls ceiling and in the garage ceiling. Do make sure you are getting enough air thru your vents as well having enough return air ducts for the room. Adding supp heat would likely solve your problem but is pricey to install and then run all the time. Your DH from what it sounds like didnt insulate the kneewalls correctly buy just laying down the fiberglass. Fiberglass insulation wONT STOP cold air from going thru it at all. Are you using the kneewall area for storage? If he can still get in there have him spray foam using a foam gun on the kneewall/floor junction and make sure its sealed off. If you arent using the place for storage insulation should only go on the actual back of the kneewall; its pointless to put it on the floor in there and the slope. He is going to need to put more than the usual r13 batts on it too and cover the area with 2 inch think r10 foamboard to serve as a good air barrier and additional insulation for a total of at least r23. If the space isnt too deep you might think about filling it totally with cellulose as i did mine. My kneewall area was 5x20ft and had a~2ft space behind it. since i couldnt get in there i just filled it with 30 bags of cellulose. Difference was immediate. The other big thing i did was go and check out the garage ceiling and found only 2 inches of fiberglass there in a 12 inch space with it resting on the garage ceiling. This left all that space above for cold air to run around under my floor. I again drilled a series of 2 inch holes thru the sheetrock all along the rafters and used a fill tube to snake past the old fiberglass and filled the entire ceiling of the garage with cellulose--again about 30 bags. The sidewalls and the ceiling of the bonuse room i did like you read about on various sites. So in the end i went from a room that we could almost never use in winter or summer to having my child sleep and play there comfortably all year long for a little over 500 bucks. Read the link below for how and where to airseal the kneewall as well as needed r values. Here is a link that might be useful: room over a garage

Well, we don't watch TV or movies to any extent. We watch football & the news. So, we went another direction in our home. We've got a large bookcase with hundreds of books (some quite rare), a chess set, wood scrabble board, cards, a small stereo system, & my piano. There's a flat-panel 15" TV. I have the custom-made wingback chair of my dreams & DH has a leather chair & ottoman. The wood pieces are all early American antique with a lot of 17th & 18th century wine glasses & decanters sitting around (DH's collection). We also don't have children home any longer so the room is no longer "child-friendly". The grandkids love to sit on Grandpa's lap in that room & play "what's it?" pointing to the various collectibles. But, it's the only room in the house where they can't roam freely. lol In years past, when the kids were still home, we've had ping-pong, tournament-size pool table, much larger stereos, larger TVs, darts, Whirlitzer juke box (really fun!), and a small dance floor. Have always had the books, chess, and one piano or another.

You are pretty far along in scheduling to not have an actual game plan here. Why have you scheduled a contractor without having a final layout from your architect? How could a contractor even give you a bid based on anything? This is not going to be cheap! And you want to pop the roof or add big dormers to try to get more floor space? Not gonna happen without more planning and at least a 100K+ budget. Your ideas do not fit the existing architecture. The whole structure would need to have the second floor removed and rebuilt.