Update on my Shimazu N/N effort: The grind is finished. Kyoto was taken on Turn 103; the game ended on Turn 107. This was a short campaign, mind you. Basically I just kept hammering away - take a province, hold it, bleed out the nearest enemy, resupply, and then move forward one province. Repeat as necessary. Eventually I was able to get financially above water enough to construct a third army, and I worked it so that all three armies would converge upon Kyoto for the final battle. It was... really bloody, to say the least.

I aim to put this campaign very much behind me - if I can barely survive a short campaign on Normal difficulty with one of the easiest factions in the game, it's clear that I have a bit of work to do mastering this game. May start my next campaign with a more centralized province.