Okay, another English-ism. Periphrasis is how English constructs many of its verb tenses, with a form of the verb "to be," called an auxiliary or helper verb, followed by a participle form, in many conjugations, so that is our English language mindset. Why not just let Greek be Greek? χαρα η πεπληρωμενη, "joy [subject] may be being [the main verb, an intransitive linking verb] having been made complete [predicate nominative perfect participle]. "In order that the joy...may be being having been made complete." Translating it this way is grammatically correct English, just awkward English style. But I think there is a nuance lost when forcing it into a periphrasis. It is a present, ongoing "may be being" (matching γραφομεν, "we are writing") sense and awareness of something that has been accomplished. What was, perfect tense, accomplished? The stuff of verses 1-3!