pcolormesh control color levels

I want to plot two sets of masked data on a single plot and I can not get exactly the kind of image I want to. I have tried pcolormesh and contourf and both have problems. With contourf the inner data does not look smooth and sometimes has a row of missing data around it, with pcolormesh, on the other hand, I can not control the levels in the way I want to.
So, as is in the documentation, contourf may have problems with masked data, so I can skip that solution. But how do I achieve controlled color levels as I can do with contourf, but using pcolormesh? Attached code illustrates the images I get with two methods.

Best regards,

contourf_probl_subm.py (2.05 KB)