It would be more comfortable if you would clarify whether the AP's interest is a "separate interest" or a "shared payment" (to adopt the vernacular).
First, my recommendation to plans is never to allow a separate interest award after an annuity benefit has started. But it does not matter if the plan (QDRO procedures, really) is unfortunate enough to allow such a thing (actuaries can solve everything relating to the numbers). Your instincts are correct either way. Can you come up with a legitimate reason not to pay the AP, given that the law is that the AP is to be paid in accordance with the QDRO? You have already argued well against my favorite reason for disqualification -- the order asks the plan to do (pay) something that the plan is not designed to do. You said that the plan could pay and has terms that say how to pay. Go with it. The payment restriction/dilemma will continue for the participant to the extent of the participant's future payments. The AP is not in the same position, so the restriction need not apply to the AP's payments.
On behalf of the plan I would be curious about what the AP knows of the participant's whereabouts. It is possible to get a domestic relations order covering an absent participant. And maybe the participant will appear now that a possible reason for disappearance has resolved.