1. Charlotte is a pretty big city. Call around for rental yards. I have the choice of about 6 within 10 miles of Redwood City, CA. Both equipment and charges vary from yard to yard. Many yards do not rent excavators with a thumb, the lowest priced yard has one with a thumb, just as an example.
2. You are going to need some fill to correct the settling problem, think that one through before you start driving. I am thinking gravel pushed down into the soft mud near the settlement, using the hoe. Decide where you are buying, how it is getting there, and what to do with any excess.
Maybe a pro will chime in, but I am thinking that replacing good sections may be asking for future trouble. If it ain't broke, don't fix it. Just do the section that has settled.
3. Before you replace any of the pipe diagnose what is really wrong. If it has just pulled apart, all you need is couplings and fill. Re-use the pipe, otherwise you have a disposal problem at the end of the job.
Good luck