Jeremy, I am going to reply to part of your comments. I am an engineer, but have not experience in designing a residential foundation restoration. In addition, design of a lifing system requires that we know more about the construction of your house (size, how many stories, framing and masonry details). What you are doing is a full foundation retrofit or re-build.
You proposed placing new foundation pads into the floor to support jacks that would be used to lift railroad ties under the floor joists to lift the house. You want to elevate the house and construct a new interior footing at the same grade level as the existing foundation. You offered a number of details on the footng for the wall. Then you were going to purchase cinder blocks and "go to town".
The major problem with your plan, other than you havn't dealt with permits or safety issues, is that the proposed foundation does not fall under the sill plates. If the house is jacked up (or more precisely temporarily supported on jacks) The objective should be to remove the interior support wall and demolish the original foundation in small sections and rebuild it to the sill plate. The challenge is to pour concrete or rebuild with block in a way that the sections tie together and become a monolithic solid foundation under the sill plates, and include J-bolts to tie down the foundation.
If you are really intent on doing this yourself, you need to retain an engineer qualified to advise you and design foundation retrofits. He will prepare drawings and specifications that will not only guide you in your work methods and sequence, but that can be used to obtain the required permits from the city of Chicago. I would think that an engineer will cost you about $1600 to $2000 of your hard earned dollars to produce this information, because they will need to obtain site and building information, and execute the drawings.
I still think you should consider a consultation with a real estate attorney to see if you have any recourse from the concealed structural defect that at least it appears, the prievious two owners were aware of but failed to disclose.
I look forward to David's input on this because he has more practical experience in actually working with these problems. So stay tuned.