Pesach - Gebrokts

Among Ashkenazi Jews, particularly those of Chasidic backgrounds, there is a significant custom to abstain from consuming any matza product that has been soaked in liquid (e.g., kneidlach/matza balls). This practice is known as “gebrokts,” or more precisely, “non-gebrokts” (lit. non-broken, i.e., not placing broken pieces of matza into liquid).   

Although some refrain from eating gebrokts the entire eight days of Pesach, there is a widely accepted minhag to be lenient on Acharon shel Pesach (the "last" or eighth day of Pesach). In fact, among Lubavitch Chassidim, on the eighth day of Pesach, the custom is to dip matzah into each dish served at the meals [Sefer HaSichos 5702, p. 105]!
 
At first glance, the leniency on the eighth day of Pesach regarding gebrokts seems puzzling. If the reason for refraining from gebrokts is the possibility of leftover flour on the matza leading to chametz, why would we be lenient on the eighth day when chametz is still prohibited? This intriguing question has led to several proposed explanations.
 
Rav Tzvi Elimelech of Dinov asserted that the issue of gebrokts is merely a halachic stringency. Since the eighth day of Pesach is rabbinic (sfeka d'yoma), if a person were stringent about gebrokts on the eighth day, it would suggest that these are not stringencies but rather a genuine concern of chametz. This would further imply that those who eat gebrokts the entire week are eating chametz! Therefore, the stringencies are relaxed on the last day (Sefer Derech Pikudecha, Lo Ta'ase 12). 
 
According to the Chafetz Chaim, because some eat gebrokts on Pesach and others don't, it precludes people from getting together on Pesach. Therefore, we try to unite everyone on the eighth day, setting aside the custom of not eating gebrokts [Dugmat M'Darchei Avi page 30:8].
 
But what about a year when the eighth day is Shabbat? Can a person who doesn't eat gebrokts prepare foods such as kneidlach on Friday to be eaten on Shabbat?
 
The Minchat Yitzchak [7:33, and Nitei Gavriel Pesach vol. 3 19:9], the Chazon Ish [49:15-16], and others permit it as long as an eruv tavshilin was prepared before Yom Tov. However, the Chazon Ish added that if one did not eat gebrokts not as a stringency but because of a genuine concern of chametz, then preparing it on the seventh day is prohibited.
 
It was reported by the late Lubavitcher Rebbe's personal secretary, Rabbi Leibel Groner, that one year when the eighth day of Pesach fell on Shabbat, the Rebbe was not happy that kneidlach were not prepared before Shabbat to be served on the eighth day. [Otzer Minhagei Chabad, ibid.]. This story is especially significant since it was the first Lubavitcher Rebbe, whose rulings are the source of the widespread observance of not eating gebrokts on Pesach.