I ended up making alternative plans (paying more, but totally changing my destinations and plans altogether) - - but I wonder now if the risk is low enough that I would have been okay to book the NYC-AMS flights I was contemplating.

I see that they - - www.openskies.com - - are still advertising regularly in www.nytimes.com (not sure what that means about their chances of BA pulling the plug)...

..but the apparent "paradox" seems to have disappeared - - of seeing fares AFTER May 31 on www.lavion.com that are the same as the promotion (which was indicated as ending after May 31)...

... the same $1250-ish fare for NYC-AMS in "prem+" ("biz-class-ish"?) is available on the first set of dates I checked, on into July.

I wonder what 3 more months (12? 24?) will bring for this experiment?