Is there wood sheathing on the exterior of the studs, with tarpaper on the exterior and a vented air gap to the stucco?
If not describe the stackup- just filling those stud bays with insulation (any type) could destroy the framing if the stucco doesn't have good drying mechanisms. There are often ways around the problem, but it varies with the actual construction.
Spray foam is on the expensive side- there are cheaper ways to air-seal, and you would still need to use other stuff (acoustic sealant caulk is good) to air seal the other seams/joints in the framing & sheathing such as between the bottom plate & subfloor, subfloor & band joist, doubled-up top plates etc. If you go with spray foam for the cavity fill, use open cell foam not closed cell, since the performance of closed cell is severely undercut by the thermal bridging of the framing. Going with 2x4 framing and damp-sprayed cellulose or open cell foam on the cavities, and 2" of foil faced rigid polyiso on the exterior costs less than 2x6 framing with closed cell cavity fill, but has about 1.5x the performance at the same wall thickness. The 2" rigid + 2x4 wall is about R23 "whole wall" after thermal bridging, compared to ~R14 for a code-min 2x6 wall with R20.
You may or may not need the Boiler Buddy, depending on the amount & type of radiant heat and the thermal mass & size of the 5-7 zones. The min-fire output of the Lochnivar WHN055 is about 10,000 BTU/hr, so it can manage some fairly small zones without short-cycling. The higher performance the building envelope, the less benefit you get out of micro-zoning, so if you make the upper floor reasonably high-R you can single-zone it.
The heat load @ +15F (the 99% outside design temp of L.I.) of the basement even without foundation insulation is probably between 10-15K, but it'll be under 2K if you put an inch of rigid foam on the foundation walls, with a 2x4 batt-insulated wall trapping it in place as the code-required thermal barrier against fire. If you're using a surplus antique radiator for the basement, find a big'un that has large volume, to guarantee that the boiler won't short cycle.
Ideally you'd like the smallest zone to be able to emit 10,000 BTU/hr with 110F water (where the WHN055 is hitting it's stride with mid-90s efficiency), or have sufficient thermal mass to not short-cycle, with no more than 3 burns/hour when serving just that zone. That would save you the cost & complexity of the Boiler Buddy. If you insulate & air seal the original part of the house (including the foundation) and install tight low-E storms over the antiques then put U0.25-ish windows and a high-R walls on your second story the whole house load is probably going to be under 25K, maybe even under 15K. Chopping that up in to 7 zones means the average zone will be only 15% of the minimum-fire output of your boiler, and the smallest zone may be 5%. It's probably better to keep the zone counts down, which will automatically keep the mass & radiation per zone higher. At a minimum you'd be looking at three zones (basement, first floor, new floor), but holding the line at 4 zones is probably reasonable.