You are not the only one in this situation. All my UN former colleagues have managed to get their ASHI coverage approved, I quote our association's focal point:
"The only proof of my Cigna insurance was the very same you attached. I had applied end of September, perhaps by then, and as a reaction to your “groundwork” earlier that month, they had decided to accept the “open-ending-date” version. I am certain, for your next attempt it will be sufficient.".
The next attempt is 5 years down the road, but never mind the alternative didn't required any juggling, so I went down the path of least resistance.