Yes, I would like to know you most efficient siege tactic for FoTS.
As Imperialists it's pretty easy, take enough units of artillery and perhaps even a full stack fleet of boats, and shoot the out of the defenders, mopping up the few survivors when actually entering the castle. This works against full stacks of defenders and you shouldn't lose over a 100 soldiers when you handle it right. It's boring as hell but sending you firearms soldiers agains a bunch of samurai on a wall is suicide. Unless ofcourse, you do have a tactic that makes you able to fight that way.
The Shogunate supporters are the ones who have a harder time attacking. Even the weakest firearm units can take out a considerable amount of soldiers that approach the walls, giving you quite a few losses even though you can kill the entire firearms unit on the wall with barely any losses if you use melee samurai.
Burning down the gate is another possibility, it kills many defenders when the gate explodes, but you will also lose many soldiers because of the gunfire, and when you finally get through the gate they just block your path with some units, so while you are stuck they can shoot some more that are waiting in front of the gate. You can use artillery on the Shogunate side, just like on the Imperialist side, but that makes it very unautentic to me, and feels just wrong, maybe a couple of units will suffice for shooting the gate or something.
What works for me is sending one unit of samurai for burning down the gate, while sending some others to climb the wall, and that way fight untill the last defender is dead, that way you have all units at their wall distracted so you bow kachi can help you as well without being shot to smithereens. You can replace the unit of samurai with artillery for shooting down the wall if you took some with you. Bow kachi can be very important for shooting on large lumps of defenders when their firearm units are in melee, if you get them in range of the firearms units they will probarly die when the firearms units are on the wall.
Cavalry is pretty useless, unless you want to enter the castle on an undefended side, where you can use your cavalry do dismount, burn down gate, mount them again and charge into battle, so they don't lose the advantage of having horses.
Anyway, how do you handle sieges, I'm talking full stack vs full stack, you can decide what units both sides use, that just makes it more interesting.
I do use Darthmod but that doesn't change the tactics you can use.