The only problem I see with this approach is not knowing what other lines drain to this damaged area. The laundry and kitchen sink would bypass it but if another source drains through that location then the damage would continue to get worse.
I went to the city to enquire about obtaining a plumbing schematic for the home so I could at least have an illustration of what's going on under the slab but they do not keep those kinds of records on file from the 60s. They gave them to the original homeowner.