Ebne. I see a different picture here. If the rafters there is already bowed at that length they are worthless. So is the ply and roof above. If you are thinking of sistering to the old joist the deflection on them will or may control the birds mouth cut to drop the new rafter down far enough below old rafter to get away from that deflection ( as crehands also mentioned ) if this ceiling is now "vaulted" Basic birds mouths are cut in depth 1 1/2" and set on a double top plate which still leaves a nailer for drywall at the top.
That being said I see your Geo. You should be min (R 19) insul 9" thick with a bafflein rafters at the low slope end and soffit are up the rake to vent to complete the venting.
So lets think of what's needed in depth to insul which controls the roof rafter thickness on a low slope roof, which in turn really beefs up the roof rafter to the point that size/height of rafter is usually moot.
tell me the roof doesn't need to come off. Can you explain why you think the roof should come off? If I were to take the roof off I might as well replace the walls also.
Ignore them they don't know that they are talking about. To fool with that bowed roof and try to flatten it out is a serious waste in manpower. A sawzall and crow bar and the roofs gone in a matter of hours. Now it's a clean slate. I see where this is going of why stop there. The only reason I can think of is the grandfather clause in old codes to new. They way we get around that is leave one wall up. Attach new walls to that and now its back to a structure. The we add/pull a permit to add the 4th wall new. They hate it buts is legal here in terminology of " structure new verses renovation permit. Just a FYI here.
So bottom line here is forgot the old roof completely. Order some 2x12s 20' set at 16"oc or 12"ocl( depending on building code there and put in a vaulted ceiling. Now you have space for R value and its now an inside ceiling "Vaulted which makes the 10 wide room look less skinny/hallway look. Use rubber for the roof and have well built/insulated structure.
You can rip some 2bys down and scab onto the inside of the exterior walls and get the insul depth that way. Now if the façade is rough then I would tear it down to sub floor and new 2x6s and new windows sizes you like and tilt in to clean easier. AMAZING how it goes from a bowed roof to a full blown addition excluding the floor. MY motto is if you start with junk then you end up half still being junk. Obviously there is nothing of real value there to save/
1. Roof needs completely replaced
2. Walls not thick enough for insul ( although spray foam can get better (R) value then fiberglass)
2. Windows are junk
Only thing left here is added façade costs.