PU solution makes no sense, not only is it not available to Muslims but Egypt's situation between 1517 and 1521 is not represented by a PU at all since there wasn't a separate government structure in place. You would have to have annexed Levant, a vassal Hejaz and Egypt with very high autonomy and unrest. In EU4 terms, Ottomans fully annexed and cored Egpyt in 1521 and their control only got stronger towards 1580s.
PU is possible through commands, and a 50 year cool down to annex by decision could be a way to simulate the increasing control the Ottomans get over the area. Fully annex the Levant, spit out a vassal Hejaz (if proper provinces are held) and keep a rump Egypt as a PU until 50 years have passed. At that point the choice is to spend Government Reform Progress to annex and fully core for free or keep the PU and integrate manually or roll the dice on inheriting.
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