I asked Cliff Goodall about this at one of his info sessions as we are also a recent Private, Nonprofit RA. He said that we can use the Notice of Non Payment method as long as our Bylaws refer to the ability to collect on overdue payments. He did say we did not have to specifically mention the use of a Notice in our Bylaws--just use a broad expression as used in the sample Bylaws. Of course, it can only be used for "members" who agreed to the Bylaws,as recorded, unlike the Statutory RA process.
He wasn't specific on wording of the Notice but I have assumed that we would use the same form but edit it to refer to our Bylaws. I don't think you could/would reference SS 3101 since it doesn't apply to non profits.