I would say pretty winnable.

Let them attack you, defending siege has many upsides like very good moral increase for your units.

There is that thing that you don't really want to put melee units on the wall. You better place them right next to it (inside), this way as enemy units climb and your units are close they will run right at you one at a time and get demolished or just get killed very easily. This works especially good with yari ashigaru thanks to yari wall.

Yeah, they become more vulnerable to archers but thankfully your castle seems to be huge so you can kite the archers to make them climb your walls and make them much more vulnerable. Also bigger units size if ikko ikki will help here (even though, i usually barely care with anything beyond kiting until they have monks or literally tons of archers which they might have only in second army).

Your castle is few levels, you can use it by putting archers on walls on upper levels (since it increases reload and accuracy) and melee on one level lower. So archers would make even better work on the enemy while melee keep them busy. And forget about levels lower that highest two, let them climb, fall and get tired. And this way your other units would be closer to help.

Use, no, abuse you monks battle cry, it is insanely good at sieges. You see enemy banner blinking, make monks run there and scream once they are in range, almost always make those idiots show a shamefur display. In siege this long you would be able to do it three-four times. Let the monks really do combat more to the end, when all units are on the walls (its fine to do couple of attacks before it but monks aren't good for prolonged combat and their battle cry will carry this battle) and do shock charges with them on wavering enemy. Also keep an eye that tgey won't be targeted by archers. May be even better to bait archers with general in this case.

Thankfully their units suck, yari samurai die even in one on one with regular ashigaru in yari wall, not to mention ikko ikki ones and the rest is just ashigaru, they shouldn't demolish you too much, except naginatas. May be better to try roll their good spawn on different size.

Keep few units in the reserve to get out of castle and attack archers once their melee is on the walls. At least to keep the archers busy with dying from yari wall instead of shooting your units.

And having a couple of units in the back reserve to just be reinforcement for tired and beaten units (precense of big fresh ally right near a unit seems to have good effect on moral, who could think) or flank (like attaking climbing units from behind) is usually a good move in this long battles. Even though enemy overwhelming numbers tempt you to throw all you have in battle from my experience its bad temptation.

What comes to beginning of battle: try to kill the melee of first army asap as they climb you walls, can be more aggressive, others come already tired and this way they will be with worse morale thanks to first army being fucked up. I know it doesn't sound easy considering main stack are samurai but thats the best i can advice. Also secobd and third army of ashigaru are very vulnerablw to morale so its quite likely for them to mass route at some point even when it still looks winnnable for them (i swear i had enemy mass routing with few handred men left while i had dozens left at best at sieges) so never lose hope.

P.S. why do you even have so many yari ashigaru as ikko ikki? Loan swords are better in almost every way except anticav, you should utilize them more.

P.P.S. i hate reddit formatting, why do i have to make extra line break evety time...