(3) Tiger of Kanto
Besides Ikko-Ikki, Uesugi Kenshin has to deal with the often powerful Takeda-Hojo-Imagawa alliance. The first two often expand north and declare war on Uesugi's vassal quickly. Therefore, if we do not want to fight Ikko-Ikki first, we may as well fight Takeda and Hojo first. In history Uesugi Kenshin met his nemesis Takeda Shingen this way. The Hojo was no match on the field and had to hide in their castle.
Taking on two "Great" clans at a time is of course quite a challenge, but since you can quickly force a peace treaty after one good battle, it is quite likely that you can divide and conquer the trio effectively.
But again, the problem is what happens next - you have now a lot of vulnerabilities. Nearby clans could easily swarm you and you might have to give up a good number of provinces.
If you wish to role-play Kenshin, you are a little too war-mongering. You fight Takeda because you want to stop their invasion to the north, not to invade them. So being a warmonger does not fit Kenshin's profile too well.
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