(In post #2, Barb made the comparisons to past perfect, by introducing "I recall ..." etc.
But it can't be "having have" because both the present and past perfect tense require the past participle. I suspect it's still present perfect.
"Peter has had a good dinner." (Present perfect)
"Peter, having had a good dinner, watched TV" (Present perfect continuous?) If that is the case, the past perfect tense is not used at all in the original sentence, and is a red herring.
Maybe philo, or some other grammarian could elucidate.