Perhaps a new mechanic entirely would be great. Something that takes mechanism from HRE, Celestial Monarchy and other things.
For example, 'Japan' would be a grouping of clans similar to HRE, led by one faction who will be the 'Shogunate'. Kind of like HRE without voting or elected monarchs. The Shogun's power would be based on 'Shogunate Authority', similar to 'Imperial Authority' in HRE. It would affect a lot of things, including probably tax and manpower among other things. The lower the authority gets, the more the vassals will begin to hate the Shogun and if it gets low enough, clans would be allowed to declare war on each other and also get the casus belli to overthrow the Shogun.
I have yet to think how to integrate the Imperial Court into this, but at least this will be better than the current system. If the Shogunate authority gets drastically low, there should be an option/casus belli to restore the emperor, who will not be a Shogun but a regular despotic monarch (absolute/administrative with high tech).
Emperor Go-Daigo also took power from the collpasing Kamakura/Minamoto Shogunate this way back in 1332.