Q. See question above. Are there any other valid and better opinions?
A. Indeed there are: Horav Isroel Lipschitz Zt’l , in his commentary Tiferes Yisroel, writes that in polar regions there is allways a 24-hour day, as proven by the fact that the sun rotates in the sky from a high point at noon to a low point near the horizon at midnight.
He does not offer a means of measuring the passage of a 24-hour day during the polar winter when the sun is invisible.[10] He advises that a Jewish traveler observe the beginning and end of the Sabbath based on the clock of the location whence he came. It is unclear whether this refers to his residence or his port of embarkation.
A result of this view is that two Jews who leave from different cities will always observe Shabbos on Saturday, but at different times. A Jew who leaves from America will observe the Shabbos according to the clock of his hometown, while a Jew from Europe will use the clock of his European hometown, which begins and ends Sabbath about five hours earlier than in the United States. Thus, there is no uniquely identifiable beginning and end of the day in the polar regions.
In some views, the time of Yerushalaim can be used to observe the Shabbos while in polar regions.
Rabbi A. Bartfeld as revised by, Horav Yaakov Hirschman, Horav Dovid Pam, Horav Aharon Miller, Horav Chanoch Ehrentreu and Horav Kalman Ochs Shlit'a