Took a lot of save-scumming and luck to beat! Definitely favors the blue faction, and I'm not positive the Hyuga faction is capable of winning, at least not with my strategies.
Ended up using the green faction to hole up in the bottom one-two and building tall, before sniping capitals with cav and then building tall again.
Quite a fun game, though! I do hope to see it possible to win in Kyushu with the purple or tan factions. I also think you're incentivized a bit too much by the random starting cash to reset runs until you have a better-than-average run.
I also ran into a bug where if you "quit" from the in-game context menu while in a demo match, the match continues on, instead of resetting to board start. I had to reload the page every time I failed in order to try again.