Seeking model # & age of J.L. Møller chairs  

Those don't look like any Moller chairs I've ever seen and it's not like they produced a great number of designs. There were only 20 or so, counting the newer ones. I don't believe they did any that had screw plug covers, but they're still in business so you could always try emailing them yourself!
http://www.jlm.dk/
Unscrupulous dealers are known to put fake labels on lower end furniture in order to get a better price and move it faster. Could be the case here.

There's the same style listed on 1stDibs in rosewood and black leather for about $1200, and I've seen 3 that have sold in different ebay sales that are the same style, but no one has the model number or specific date of manufacture. All 6 of my chairs have the Moller label. I emailed the Moller company late last week but have not yet received a reply. I'm using my phone now to post this so cannot provide links until I get home.

By the way, my husband has made furniture both as a hobby and professionally off and on over the past 40 years and he says the quality and workmanship of this set is excellent from a craftsmans point of view. It's beautiful to me too and seems well made and sturdy. I despise cheap furniture!

Hmm! Well, I hope you year back from the Danes and please do a followup, whatever you hear!

Ah, I think I saw one of these once. It is definitely later.

Here's the one on 1stDibs https://www.1stdibs.com/furniture/seating/armchairs/niels-moller-danish-...