Nice question, but maybe for nonlinear time (or response) history analysis you do not need to overcome the convergence failure, at all; in brief the reason is the fact that in these analyses the inaccuracy is under the influence of both time step size and the nonlinearity iterations, and these two sources are mostly independent. Have a look at "Soroushian, A. and Wriggers, P., 2023. Elimination of the stops because of failure of nonlinear solutions in nonlinear seismic time history analysis. Journal of Vibration Engineering & Technologies, 11(6), pp.2831-2849", and if needed be in contact. I need to leave now. Have a very nice day.