Carth,
He has his army on the Border of Kaga, ready to take it. Taking Kaga and Echizen still yields a front to his south, but now instead of it being a bitter rival, it'll be some clan he hasn't met yet, which means it could be more trade and a neutrality of sorts- plus he can get ride of the Ikko temples that are surely causing unrest in his provinces(and of course one accuracy prov and one smithy prov with fertile fields). I don't think he should turn on Hatakeyama at this point. He is already at war with 3 clans. Hata is his ally and currently a distraction for Takeda. Allowing Hata to remain that distraction while finishing off Ikko(and possibly Kiso) makes much more sense. He should easily be able to take down to Echizen, start building accurate/armored armies there and at the same time build up a strong army out of Iwate.
Then he can crush the Takeda from the backside through Shinano. And then when Takeda is broken, his armies will be in position to vice Hatakeya. Then he can scrape those 2-3 armies down the east coast while still building more armies in a prime spot on the west.