As the test is in good agreement with Abaqus for the isolated moment, I would proceed as follows:
1-Check if some BC may have change from moving from Step 1 to Step 2.
Inspect how reactions evolve at the Boundary and if they are all in balance and as expected compared with the input forces/moments. Specially between the end and beginning of each step.
Are you using Perturbation parameter?. Are you redefining the BC in the new Step?
2-Check if contact state may have change from moving from Step 1 to Step 2.
Is the contact clearance maintained in-between steps without additional loads?
If traction is responding as expected, the problem could be in the tangential direction.
Have you set up tangential stiffness or Friction in your contact parameters?. Are they the same values as Abaqus contact parameters?
How do final CDIS and CFS compare with Abaqus?.