I'm going to try these:

-newtonFTol=value or -newtonFTol value
    Tolerance respecting residuals for updating solution vector in Newton solver. Solution is accepted if the (scaled) 2-norm of the residuals is smaller than the tolerance newtonFTol and the (scaled) newton correction (delta_x) is smaller than the tolerance newtonXTol. The value is a Double with default value 1e-12.

-newtonXTol=value or -newtonXTol value
    Tolerance respecting newton correction (delta_x) for updating solution vector in Newton solver. Solution is accepted if the (scaled) 2-norm of the residuals is smaller than the tolerance newtonFTol and the (scaled) newton correction (delta_x) is smaller than the tolerance newtonXTol. The value is a Double with default value 1e-12.

adamLange wrote:

Is this right?:
  - there are different tolerances for the integration step and for the non-linear solver. 
  - there is a default tolerance applied to the non-linear solver.
  - an appropriate simulation flag must be passed to override the non-linear solver tolerance.

Yes, and you found already the correct simulation flags to tune this tolerance.