Thanks for taking the time to report back.

Glad AF La Première First on award still allows access, that's a nice start of the journey.
When it comes to a First Class lounge in AMS:
there are none so do not even bother to find solace in the alternatives of
the non-schengen OneWorld lounge /
schengen Star Alliance lounge /
and both schengen & non-schengen Aspire lounges,
and both Crown Lounges in schengen and non-Schengen
I cant comment on the Privium lounges as i do not have Privium.

Or oops i suddenly thought....
One could actually think that KLM would maybe allow AF La Première First customers to enjoy the exclusive Flying Blue Ultimate private room.
No idea, as my one and only time on AF La Première First was in 2015 and the exclusive Flying Blue Ultimate private room is just recently installed.

About the service flow at the VIP centre,
i agree their core business is to provide a discrete seamless travel experience.

It is however an independent entity not owned/ affiliated with any airline
while as the AF CDG La Première lounge is part of the total AF company so has a better streamlined connection of AF flights operations.

I can agree that service can be sometimes flustered / offkey,
as a personality can be insitu with a crown / harem / diplomatic / celebrity that has churned out unexpected demands and requests.
I tried to match such dignitaries by travelling with a rabbi, nun, nurse and priest but one cannot outmatch above personalities in pecking order

As always, thank you for sharing ... now i do need to find a destination suited to use AF CDG La Première lounge based on your recommendation to compare