I once encountered a similar issue with the simple mode because my mesh was very poor (max non-ortho angle 68°, with max skewness 4.2)
A very crude fix that worked for me was to first start the simulation using very strong under-relaxation (e.g. 0.3 for all equations and fields) and the most stable first order schemes. I then let the result converge, the result was questionable at best due to the poor accuracy, however, after switching to 2nd order schemes from there, the simulation was able to reach the result we were looking for.
Another crude fix could be to increase the number of loops you go through for each iteration (nCorrectors, non orthogonal correctors, outer correctors).
Numerical instability usually points towards a bad mesh, so maybe it's more time efficient to go back and refine it further before attempting anything else.