Is it even possible to win as a Republic on higher difficulties?

[AnthraxPopsicle]

I have tried to go Republic with the Satsuma and Tosa clans and just can't seem to hold my footing against all of Japan. I suppose I should find out how many territories I have to take before the realm divide is triggered and reinforce all of the territories I have at that point to the Star Fort/Gun Battery level and research all naval techs.

Anyone have any other ideas?

[Saunen]

I Haven't tried it yet but I've been alone in both my Nagaoko and Choshu game vs the rest so i don't see why it would not be possible.
Ultimate garrison would be a fortress, barracks, market, police station, not sure what lvl of city but whatever allows 3 buildings.
This garrison (1 spear levy, 2 levy infantry and 2 line infantry) is pretty much unbreakable in siege defense, in my Choshu game i went with 2 units of levy infantry (so 1 spear and 4 levy infantry in total) instead of having a barracks and added a cottage workshop instead also held its own but against certain armies it wont hold (such as full shogunate/imperal armies), It will beat down any rebels though.

Now your armies can roam free, also in my Choshu game i had no navy untill about 72 (would not suggest this, your economy holds up but repairing bombardements get way to expensive in comparison to beating the AI fleets early on).

number of provinces anywhere between 5 and 15, key techs kneel fire & suppression fire.

If you just wanna get it done without any houserules id suggest choshu with 6-8 kihetai and 2-4 parrotguns +1 general per army, Or Saga as they start with a parrotgun which helps out the first 20 turns but youll have to make do with line infantry instead of kihetai.

[Babaganoush]

I did my Campaign on Hard as a Nagaoka and completed my Republic. It's extremely hard but possible.

My tip is to use your Shinsengumi/Ishins to revolt as many provinces as possible, preferably adjacent to your frontlines and use those rebel areas as a buffer zone to get ready for the RD.
Also get ESSENTIAL territories pre-RD. What I did with Nagaoka was rebel the northern east-Honshu of Japan and occupy the southern parts so I could build a railroad network without triggering RD quickly.

Get all the lower costs/higher tax and repression/happiness bonuses as a priority. Also daimyo honor. Higher honor = Happiness bonus for your provinces. TBH, I conquered Japan with just line infantry and parrot guns for the first half of realm divide so that military tech should be the last thing on your mind.

Explosive shells and ironclad boats are a must though. The most annoying thing was protecting my north and south borders as I pushed forward.

I heard vassals turn against you immediately since they dont switch to Independent even though their lands could be independent supporting populace, but I'm not sure.

[Cruzz]

Finished one legendary republic as Choushu, failed another one with Saga (permanently bombed trade port + getting nearly all of your generals and agents assassinated within 2 turns wasn't a good combination). A couple of random tips based on this:

1. Don't have more than 1 trade port when you're going republic. Build this trade port in some province where you can block the AI from bombarding the port with a single fleet (with single ship fleets in reinforce range to increase range if necessary). Basically do NOT have the trade port in a location like Saga's home province which is the absolute worst shaped port province ever. Losing your trade port is a large hit on your income (foreign trade) and any odd AI fleet will blow it up, while military ports and drydocks often can hold out for a while against 1-2 ship fleets and don't really affect your income when destroyed anyway.
2. Preferrably have a police station, upgraded castle (not up to star fort as that reduces happiness) and gambling den in every secure province (ie. one where troops are wasted) before RD. The unhappiness from being 100% the wrong alignment is nasty after RD. I'd also recommend the happiness techs if you're playing a long campaign, but they're not worth it on short.
3. Looting is your friend. You only get -3 honor at maximum from looting, every looting is "free" after that.
4. Don't autocalc fleet battles if you don't have a general in the fleet, your ships take so much damage you really can't afford with the autocalc. Also, generals level up really nicely in fleets and are safe from agents so I do recommend mostly keeping them in fleets.
5. If you have the chance, try destroying as many small clans as possible before and after RD. Small clans will try to attack you with armies delivered via ship more or less just as often as large clans, so you're better off with a couple of big opponents over lots of small ones. Also it helps with the agent spam.
6. Depending on where your provinces mostly are, you may want to prepare blockade fleets before RD to immediately start blockading enemy ports after RD. If you're playing a Kyuushu clan you definitely should blockade off all the three one-island clans near you if you haven't conquered them. Also fleets placed at straights will stop the enemy from being able to cross with land armies, sometimes useful around Shikoku and Kyuushu.
7. I'd go for iron plating before building any real fleet. Ironclads are just that great. Frankly speaking you can do just fine without any of the ammunition research, never got them myself.
8. Everyone, including your vassals, will turn against you within a few turns. At most some clans might take 3-4 turns before declaring war against you after RD. But you should still establish a single vassal during the game for the +1 honour.
9. A couple of good melee units in siege defense are nearly impossible for the AI to beat, the poor thing. For ranged units it's generally better to avoid being on the walls if you're outnumbered by tons, instead stand (well) behind the walls in a very thin formation and just pick off AI units as they finish climbing up. You're likely to get to "enjoy" a lot of silly fights with a handful of units versus stacks of units if you end up playing legendary republic.

[darknessfalls]

The main issue with republic are those first few turns (except on legendary with cheating AI). If you are willing to sacrifice a building slot, going for the gatling gun upgrade for castles makes the game almost lulzy. Bare garrison can hold anything but a full stack with arty support. I like doing this in key provinces like the connections to the mainland from Shikoku or Kyushu. As someone else mentioned, use the last of your ishin/shin agents to incite as many revolts as possible. Even cheating AI will take some time messing with those and can even have some interesting effects if you control the situation right.