1. Dual suns (possible but NASA won't lend me spaceship to check)
Well at some point on the surface of the Earth (well a ring) you would be able to see both suns, as two suns have never been seen we can rule this out.
2. Antarctica tours are really just trips to the arctic circle (BINGO!)
But if they leave from somewhere like Tasmania, or New Zealand, then you can work out the speed you travelled by the distance and time. As the time is known, and the distance to the Arctic Circle is also known, you can work out the Speed. You can also check the speed of the boat in many different ways (as compared to the waters of the ocean, or better yet as compared tot he change in angle of the stars. That last method can be checked against measurements made on ground and so eliminate any errors that might occur due to "Fish boosts".
But no such high speeds have been recoded, so we can rule this out.
3. Sky mirror scheme to bring sun to ice wall 24/7 (very unlikely)
I agree this is very unlikely, but as the other two methods have already been ruled out, this is therefore the most likely of the scenarios
you posted. However, if Sky Mirrors were bringing sunlight to the Antarctic, you would have to reflect the Sun, which means that you would get multiple images of the Sun, which suffers from exactly the same problem that your first scenario suffers (mainly that at some places you will see more than one sun).
As multiple suns have not been seen, we can then rule this out as well.
So not one of your scenarios actually stands up to a reality check.
None of them reflect reality. So none of them can be correct.
But RET easily explains it all.
I will accept the one that explains it, and not one that can't.