Yischok or Yitzchok

A friend of mine pointed out to me last Friday that in the krias shem at a bris, we say in the middle אֲשֶׁ֣ר כָּ֭רַת אֶת־אַבְרָהָ֑ם וּשְׁב֖וּעָת֣וֹ לְיִשְׂחָֽק׃.  He wanted to know why יצחק was spelled with a 'ש.  I pointed out to him that that's  what it says in Tehillim (105:9,) which is the source of that line.  According to the קונקורדציה, it is spelled that way 4 times in Tanach, in the also verse of Yermiyahu Ch. 33, this verse in Tehillim and twice in Amos Ch. 7, verse 9 and  16.  The Metzudos Tzion in Yermiyahu says ישחק. יצחק כי זסשר״ץ מתחלף:  However, what is the significance of this change?
The Yalkut Maom Loaz in Yirmiyahu brings from Chazal:

                                        A different interpretation is given by the Mincha Gedolah in Amos (7:9.) The possuk there is talking about the bammot made for avodah zarah in the land of the ten tribes.  He quotes from the Alshich that the 'ש in place of the 'צ comes from the name of עשו.  He explains that Yaakov is already connected to Esav via the 'ע that exists in his name and the 'ו that sometimes appears in his name. Therefore, when referring to the tribes that did the actions of עשו it adds the connection of the  'ש in the name of Yitzchak.  The problem with this explanation is that it doesn't seem to explain why the possuk would switch in Tehillim and Yermiyahu.