You're in north NY where the frost line is around 4' in winter. Everybody up north build basements because it's less expensive. Sounds like the builder that built this house was a tract builder building on slab to make the most profit. To be honest, what's left looks like junk IMO. IMO, find out what the GC would charge to build a basement. Basements are on slabs which are cheaper than crawl spaces. They ARE cheaper to build but most GC's won't admit that to increase their profit. If you are not committed to this GC, get several quotes.

'Level the basement subfloor and pour a 2” ratslab

• Add 1-2” of rigid foam to the interior of the basement block walls.

What are you talking about? You DON'T have a basement. You might want to look into ICF. ICF can reduce your HVAC cost dramatically. Initial cost(allot lower seer) and monthly cost.

"Basements are on slabs which are cheaper than crawl spaces. They ARE cheaper to build but most GC's won't admit that to increase their profit."

Jesus, your back with your same rhetoric. Where can you have a full basement, dug and poured for less dollars than a crawl space? Think of the logic there, more work to dig, more concrete to pour, etc, etc, it is impossible for a full basement to be less dollars overall than a crawl space.

Adding anchor bolts to the top of foundation, parging exterior foundation, and adding foam to the interior of crawl space is a must and required by most building codes in cold climate regions where frost is present during the winter season and also insulation should be dropped down the crawl space slab.

I always add foam and also under the slab of any crawlspace.

It seems you need the existing height in order to access the crawl space and get ducts in. I'd reset loose block, parge, and insulate the walls (I think you'll find code is 3" XPS minimum zone 5). The existing block job looks sketchy so filling cores at 6 ft. on center would help, but is not a code requirement. The wall insulation is required to extend to top of footing. You'll need a vapor barrier and something to hold it down on the floor, so 6 mil poly and clean #1 stone on top is the least expensive. A rat slab is nice but not necessary. Anchor bolts are required.

It would require near surgical precision to demolish a home without some damage to the foundation. An experienced contractor would have included in the contract price an amount for any necessary post-demolition repairs (this is a good application for a cost allowance.) The lack of insulation in the crawl was something that could have been determined during design and the cost included in the contract price. Taken together, you're getting hit with costs that could have--and should have reasonably been anticipated and included in the contract scope of work.

I'm not sure that removing any courses of block makes sense if the plan is to run ductwork in the crawl space.

The crawl isn't all that tall and there doesn't appear to be any differential backfill, so I don't see the need to go crazy with rebar.

OP, "we know we shouldn't skimp on foundation, so we would really appreciate any advice".

You know it.

Don't skimp. Start from scratch and don't be constrained on such a trivial matter.

I've torn down many old homes with nary a thought of working with someone else's old and outdated foundation.

A frost-protected shallow foundation, such as the one here

--not an endorsement of the installer--is the way to go. There are other ways to frost-protect.

Costs are local. But even if it's more to do it right, I'd take that route. (Incidentally, instead of paying the contractor to remove the blocks, you'll very likely get it done for free by giving the blocks away on Kijiji etc.)

worthy, are you saying you can build a house up north where the frost line is 4' deep with a small crawl space as if you are in the south of the US?

mill.... I KNOW a basement costs more than a 'reg' crawlspace!! That's COMMON SENSE!!!!!!!!!

"Basements are on slabs which are cheaper than crawl spaces."

Then what was that quote supposed to mean?

Good pro advice prior to this. I'll pile on.

Either repair the foundation as recommended, get recommendations from a structural engineer and do that or build a new foundation. I do like retaining the height, but have the contractor explain why. I would be filling 100% of the cells.

It would require near surgical precision to demolish a home without some damage to the foundation.

Yes, this ^^^^ is exactly what our builder told us and convinced us to nix the idea of rebuilding our storm damaged home on the existing foundation. In the end, we did a complete tear down and are building from scratch. It's a hard pill to swallow but I just don't see anything truly worth saving on what you have and wouldn't feel confident about getting more than 1/2 way through trying to repair this before finding some other issue.

are you saying you can build a house up north where the frost line is 4' deep with a small crawl space as if you are in the south of the US?

I suppose one could include a conditioned above-grade "crawl space." But according to the OP, "we don't need the crawl space."

Here's the introductory paragraph on the US Housing and Urban Development publication Frost-protected Shallow Foundations.