OK, it looks like I have been officially pulled out of DDF retirement
I just sent Dan an essay which lays out most of the issues. I am just making a couple of brief comments here on some of the posts above:
Does that really only happen once a year all around the area near the pole, or does the sun make several passes skimming below and above the horizon around the equinox in those areas away from the exact pole?
At the exact Poles, it happens once a year only.
For where we were going, the only shayla was for Lubavitchers.
The bulk of the issues only affected Lubavitchers. But the issue of the absence of Tzeis would have affected everyone.
Especially since the Rebbe is a known "fan" of the Minchas Eluzar. 
It is true the Rebbe was a known "fan" of the Minchas Eluzar, but on this point, he clearly disagreed. See Igros Kodesh Volume 2 page 94, Toras Menachem 5746 Vol 2 page 847.
I've been a Zmanim enthusiast for many years now and was well aware of the שקיעה אמיתית concept but it seems like it's only recently that it's becoming mainstream to use it for calculating regular Zmanim such as סוף זמן קריאת שמע and פלג המנחה Lechumra.
It has become more mainstream ever since Chabad.org has adopted it as their default option. But it is not the consensus, and ppl should consult their Rav, or adopt the stringencies of both opinions (which is generally not such a big deal, as the difference is minor unless you are near the Poles).
That's an interesting one. Seems like most (although certainly not all) Chabad Rabonim go L'Chumra for both so they probably told you to keep Shabbos from Shkia Hanireis until Alos as well as by polar Zmanim if that's an option. (If that even makes sense. I'm not so well versed in polar Zmanim.)
But that would lead to problems where the two models are mutually exclusive. For example, Licht Bentchen would be close to midnight according to Standard Zmanim, but before 6pm true solar time according to the Ben Ish Chai’s Polar model. This leads to a conundrum: If you light before 6pm, this will be way too early if the Zmanim do in fact follow the Standard Zmanim. If you light shortly before midnight, this will be way too late if the Zmanim do in fact follow the Polar Zmanim model of the Ben Ish Chai.
Same shaala when traveling to HKG on the polar route and night doesn't fall, Summer, or the sun doesn't rise, winter, and you arrive two days later...
Indeed, transpolar flights are a major issue and many people don’t even realise. I am BEH working on an updated write-up about this.
