My torque converter failed on my '11 Yukon 3 weeks ago and the symptoms were similar with RPM jumping, trouble finding and staying in gear and for the prior couple of mos., a noticeable hard clunk on downshift from 2nd to 1st when coming to a stop. Your stabilitrak error is a separate issue.
If your TC is failing, you will need a rebuild. You have metal fragments throughout your entire system including the radiator and trans cooler/cooler lines that will need to be flushed with special equipment. It's not a simple diy and will require TCM coding if you swap in a different rebuilt unit. Find a reputable transmission shop to handle a rebuild and ensure they upgrade components to address known failure items. I paid $4300 for my rebuild.