Can a P.O.A. collect on unpaid membership assessments after the four years limitations?

The HOA probably cannot sue for assessments more than four years late. However, in their application of your present payments, the law requires them to apply your first payments to delinquent payments. This is a fairly new law, and I am not sure whether that you can "waive" that requirement in an attempt to cause first payments to be applied to the assessments that are less than not four years late. That would require further research. Even then, I am not sure there would be any reported cases on the subject yet.