During the high middle ages the Shia Caliphate/Fatimid Caliphate was located in Egypt and with it the majority of Shia Islam & its powerbase. At the same time the Sunni Caliphate/Seljuk Sultanate was located in Persia/Iran and with it alot of the Sunni powerbase.
In modern times we see the situation is reversed with Iran being the centre of Shia islam while Egypt is sunni with shiites being less fortunate in the region.
How did this transition happen? How did Shia islam move to the location of the Sunni centre and vice versa? How did they completely swap locations like this and how long did it take?
I think this is a misconception. The Fatimid Caliphate may have ruled Egypt, but the Shia population of Egypt was always miniscule. The Fatimids themselves were Ismaili, today a relatively minor sect even within Shiism. The largest Ismaili group today are the Nizaris, who were once the "Assassins", who broke off from the Fatimids and today follow the Aga Khan.
The Fatimids also had Shia contemporaries to the east in the 10th and 11th centuries, the Buyids, who were then succeeded by the Seljuks in the 11th/12th centuries. The subsequent overthrow of the Fatimids by by Saladin in the 12th century is part of why the 12th/13th centuries have been termed the "Sunni revival."
So the two things I would note is that there has always been some degree of support for Shiism in Greater Persia, particularly in Southern Iraq. But the real change comes about as a result of the Safavids, who really made an ideological effort to enforce Shiism as the official sect of their Persian empire.
They never switched places. The Shi'ism adopted by the Safavids of Iran is twelver while the Fatimids is Isma'ili (7er). According to twelver shi'ism, Ja'far al Sadiq (6th revered imam) claimed his son Musa to be the 7th revered immam. The Ismai'ilis, believed that Ja'far al-Sadiq claimed his eldest son, Isma'il as the 7th revered imam. Fatimid Egypt, went into exile and traveled from the levant to north africa then egypt under this claim to Isma'ili lineage, eventually building the city of cairo, and claiming a dynasty in modern day Egypt. As for Iran, just like the Fatimids who used a religious linage to claim their dynasty as leaders of the muslim community, the saffivids, lead by Ismail I, rallied up his Qizilbash followers through twelver shi'ism claim, eventually converting the majority of Iran to Shi'ism.