Basements, Attics and Crawl Spaces - Need some information

I'm in the process of a major home renovation, and we came across a problem that I'm getting conflicting advice. My basement was constructed in 3 diffrent sections over the years using diffrent materials in each. We currently have the front of the house jacked up to take pressure off of the oldest section (fieldstone/riverstone) to resupport the wall and repair sections that were collapsing. When they built the second part of the basement and added onto the house, they used 1' x 2' x 1' limestone blocks to make the foundation wall, and to help support the weight of the additions, they continued the limestone wall on the oustide of the original rock wall and placed a 1' x 2' x 4" limestone cap to spread the weight of the house onto the rock wall and limestone backing.

Before the work started, they escavated in 2 areas around the house to check on the condition of the foundation, and both areas looked well enough that it was thought that only a few repairs needed to be made. When they started the full escavations, it was discovered that many of the limestone blocks are worn down to the point of being unstable and needs to be replaced instead of braced and sealed like originally thought. One of my contractors says that I should have the limestone blocks removed and have a concrete wall poured to support riverstone/fieldstone wall. The reasoning is along the lines of that the stone wall has already settled as far as its going to and just needs to be braced to hold the houseweight. The other contractor advises that I pull both walls down and just have a concrete wall poured. After that, drill connecting rods to connect it to the basement floor and seal the joints.

I'm getting 2 sets of advice on this, and I trust both contractors since I've had them do major projects for me before. I know I'm paying either way, but the contractors are violently disagreeing with each other on the best long term fix.
Is there anyone out there that has run into a problem like this? And what would be the best fix? Any advice would be appreciated.

This is primarily a DIY website, and yours is not a DIY job. That said, no one here could give you accurate advice without firsthand onsite knowledge of your situation. If you question either of these contractors, get a third opinion. My suggestion would be an engineer with a background in foundations.