Suggestion:
Why not have the Taj Mahal require absolutism? Although the Moghal government was not similar to the European Absolutist states, the Moghals under akbar were the second, (and by far the most prominnet) state in South Asia to introduce a parrallel Civilian and Military Adminstration for thier state and to have an organized "nobility". What I mean by this is that Akbar arranged his government into a civilian adminstration, (this includes people like tax collectors, regional governers), but in addition to the civilian post assigned to a gov't servant they were also given a numbered rank in the Military system, and additionally would be responsible (in times of war) for mustering a certain number of troops. Akbar also reformed the nobility to include Hindus (which islamic states before the Mongols seldom included in high government posts), refomred the Moghal taxation system, and tried to create a state religion centered on his person.
So in the sense that the Moghal Empire was not a "treaditional" south asian state, the same way that Lious XIV (i hope I got the numbers right) "the Sun King's" France was not a "traditional" european monarchy, there is some room for anology. ALso the dates match up better; the taj mahal was built before the British used steam power.