I never really had a problem with lowering influence, just insult some of them daimyos and they will start hating on you.
Es gibt keine verzweifelten Lagen, es gibt nur verzweifelte Menschen. (There are no desperate situations, there are only desperate people.)
-General Heinz Guderian
Taking all provinces surrounding Kyoto dismantle Shogunate system. Can be done in two wars by anyone from outside world. This holds true for 5.1.
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Really, the problem reported on that thread is not related at all with the japanese mechanics, i remember something similar happening to me when i was playing for HRE unification : I lost any PUs i had with other HRE members after the reform to make all members my vassals, i also didn't keep any juniors of my new vassals after i unified the HRE, of course.