Thanks for the comments and suggestions so far.

Apparently my Status and this fare really don't care much clout. Rudely put: Nobody gives a f... which is strange, because I am certainly far from becoming Premier, yet I have had some very expensive work trips on BA and AA in the past and they certainly made a few dollars on my travels (if maybe not on this trip). And somehow I naturally managed to obtain Status in the past as well - this was my first ever attempt of a TP run.

13 hours and I am still at the airport. Spent two more hours on the Phone with AA and IB and got... little further.

Speaking to BA, I was indeed booked on the 8:25om LAS-LHR. But it wasn't confirmed.

AA changed the "no go" to a "go" and apparently put some kind of "approval for reissue" in the ticket. But still Iberia would have to do it. Spent another hour on the phone with a very kind employee in Lisbon. At the end, she managed to look up a good enough routing for tomorrow... just couldn't ticket it. No Supervisor to approve for the next 6 hours. And only towards the end of the call, we realized that this STILL isn't the end of it, because she may have to charge the change fee after all.

Tired and seeing my last chance to get out tonight, I had to call AA again to make absolutely sure that they understand where I see the blame, and while I was playing nice all day, I will have to seek compensation now. I will miss (at least) 1 day at work, nobody wants to put me up in a Hotel Room, or rebook me free of charge... There will be costs associated with my stay, and I will seek compensation for those. In court if necessary. I am and have been very patient and respectful, willing to negotiate and in return I am... being ignored and left behind. Nobody had an answer to my repeated questions whether I am expected to sleep at the airport, whether I will get home tomorrow, or the day after, or ever...

It's ridiculous and I don't understand their behavior at all. They leave me in a grey area. It could be simple: Tell me I am a no-show and I should foxtrot oscar, or tell me that I am right with my claim that I was involuntarily denied boarding and as such deserve rerouting and a right of care. Not "Yeah, the check-in staff put a note and you can be rerouted, but we don't know how."

I couldn't book the BA flight with Avios anymore, as midnight passed in the UK and "we can only book flights up to 0 days before departure" (online), the BAEC Hotline is now closed both in the US and in Europe and the airport staff can't do anything with Avios.

Fun fact: On the last check with BA my flight was showing as "confirmed" -
"I just need a Ticketnumber to check you in".

This is turning out to be a real drama. Not sure what to do. Terribly upset with AA which I really used to like. Customer in need: How about helping first and reading rules later?

My impression is that a few people genuinely tried to help. Unfortunately those were sat in call centers and stopped either by their Systems, or their Supervisors. And at the end of the day it is this Fare that keeps getting mentioned, "You have a very special fare" "We can't get this price" "We don't see the rules" "Only in France" "AA can't do anything to this fare" "Since you are using a private fare, I have no way to know how many months this is valid" (actually the term "Private Fare" came up very often). I am tempted to say error fare. My uneducated guess is that nobody is seeing fare rules, because they don't exist in the first place.

Anyone traveling on this in the future, don't cut it close like I did, allow plenty of time and make sure you don't get into a situation where changes become necessary.

Will look for a Hotel now, do some research on redemption possibilities for tomorrow and try to relax for a few hours.

I believe that something like this would never happen on BA. Two options (both of which I experienced):
- You're a no show, bad luck.
- We made a mistake, here's your new ticket. On an offline carrier where needed.