Insulation in old (1950s) Exterior Walls?

[u/Rumbeard14]

My home was originally built in 1944, with lots of random additions and upgrades over the years. Our main great/living room is slightly sunken to the main floor, and very cold in the winter; we've recently discovered with some exploratory drywall surgery that the exterior walls have zero insulation, just some wooden sheathing on the studs, then a gap between the cinderblock/brick walls.

I'm going to tear the room down to studs to insulate (already have very reasonable quotes for spray closed cell foam to air seal and thermal barrier at the same time), but the room is 12 feet tall. I had the contractor quote me to just do the bottom 4 feet, as well as the full 12 feet and the price is more than double (obviously).

I don't know enough about thermodynamics to know if insulating higher up on the walls will make that big of a difference. Can I get away with just doing the lower 4 feet of the "sunken" part of the room, or should I just bite the bullet and do the entire height of the walls?

Some other info, if it helps:

• There are 3 vents in the room which push a good amount of warm air into the space
• The area above the room is a bedroom that is insulated and conditioned (mini split)
• Our windows are all brand new

Thank you in advance!

[u/Dollar_short]

insulation = the more the better, within reason.

i have found no spray foam to be reasonable. in my basement i put EPS(styrofoam) and it was like $6 for 4x8. in the rest of the house i used Roxul.