I simply build hugely huge SODs of Samurai Arqubushers, and then load them on 30 transports filled with them and armies of them to go and storm their capital, as well as 5 transports filled with fire cannons.
That way, you will be able to use the cannons as primary bombardment units, and then the arqubushers are secondary bombardment units, only if the cannon fire isn't enough.
And on a side note, bringing along a Yamabushi army for pillaging, and a few Arqubushier armies for just plain destruction doesn't hurt much.
And don't forget to initiate siege on their capitals if is too hard. I once needed to destroy a capital that is size 13, and a direct assault was too costly. -- I already lost 10 transports filled with Arqubishers and only killed 10 of theirs. So, I blockaded the ocean, pillaged the land, and then starved it down to size 1, shooting at them all the time with cannons and arqubushers.
Then I killed them with hordes and hordes. (I think 200 arqubushers, or something.)