Dense fill cellulose insulation retrofit on 1939 Lannon stone

Hi GBA Community,
I would love some opinions on insulation/air sealing my old house.
I have a 1,800 sqft 1939 tudor revival house with Lannon stone veneer in Madison, WI. We love our home and want to improve energy efficiency and comfort, but not at the cost of long-term durability. Knowing our natural gas furnace doesn’t have too many years left, I am feeling the pressure to lay the groundwork necessary to prep for a cold climate heat pump. First priority seems addressing the areas most impactful on overall heating/cooling load before appropriately specifying that system. I’m planning to address several elements, but the largest question I have is whether to insulate the exterior wall cavities.
The wall assembly from exterior to interior is: masonry block (limestone)–>small air gap–>Cellotex sheathing–>2×4 balloon framing with empty stud bays continuous to the attic–>Cellotex lathe and plaster. I’ll attach one photo of the exterior wall cross section from a recent remodeling project (though this was at an old window opening and the gap from mortar to sheathing may not be consistent with the rest of the house). In all of my investigation and projects where I have had walls open, there has been minimal signs of bulk water infiltration or deterioration of any of these components.
Because of the character and aesthetic of the stone, exterior insulation is not an option. A complete gut of internal walls is also not an option at this time, so I am looking at a retrofit with intact walls. From my research it sounds like blown-in dense filled cellulose is a viable option that can insulate and simultaneously air seal. There are a variety of local contractors capable of conducting that work. Given my wall assembly, though, is this method advisable with long term durability in mind? I don’t want to insulate only to reduce drying potential and lead to future rot.
Thanks to the community for any advice/ opinions on this particular scenario. Also, are there any recommendations about who to go to for official consultation?
Adam
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