Euh...I'm not sure if you can change your state religion, I mean through any possible way to do this and keep the achievement active, since I think diplo-annexation is available within the religion groups, say you are Animist you can so diplo annex Shamanist and Animist but not Shinto
In my case there was not too much to be noticed if I understand the mechanic correctly, I was Ming, after conquering neighbouring nations I became enough strong, I found that the proper japan is de facto an OPM, so I sent some gift and ask if they wanna be my vassal, they accepted and 10 years after I annexed
the only detail I found maybe useful here is that "once the emperor itself does no longer exist, all daimyos will became a normal state as all the others"
if you can shift yourself into eastern Asia religion group(Buddhism/Confucism/Shinto/Hindu), IMO that wont be a problem for you to achieve diplo-annexing the emperor, then daimyos will be just a case of time
I'm not sure if Animist nations can change they're religion, so I may be screwed...