i think Sasaki Kojiro is referring to the fact that Shogun was originally a strategic boardgame loosely based on the novel by James Clavell...

with Shimazu (and i didn't play them much cos i found them too easy until you reached the 'Hojo Horde' point, then i found the attritional warfare boring) you should use a lot of shinobi (preferably from Tajima for the honour bonus) to destabilise and invade eastern Japan while your western armies are around the Yamashiro/Shikoku area. Start as soon as you can, concentrate on invading lightly defended provinces by sea and wiping out or appropriating heavily teched up Hojo (or former Hojo and now in the hands of other clans) provinces. This will remove the threat of meeting nastily teched up Hojo/Uesegi armies coming the other way, and will also remove the threat of a high honour Geisha turning up and wiping you out. Shimazu get lots of good heirs, but i hated having my best generals systematically hunted down.
It does lead to a war on two fronts, but your economy should be nicely built up by now, try fomenting rebellions and then bribing rebels. slash and burn to get the initial money, but then try to conquer and keep the pressure up on both fronts. good luck!