In the Uesugi 1530 campaign I find Kozuke to be a poor place for my HQ, so on the first turn I raze everything for extra starting koku and move all my troops into Musashi and rebuild there. Musashi is rich and much easier to defend with the river. Abandoning Kozuke creates a vaccuum and thins out the rebs nearby a little as they move in to occupy it (with one unit, which doesn't threaten me in Musashi). I bribe Shimosa asap, another river province and easy to defend, and this creates a nice defensible front. I then take Kazusa (which provides better emissaries), and bribe Shimotsuke, Hitachi, and Mutsu (Mutsu having a nice collection of troops) as soon as I can afford to (being sure I have additional troops or shinobi to add to the garrisons, to avoid rebellion). I try to bribe Dewa too, as there is a unit of No Dachi there which is handy to have early on. As you described, once I have the Eastern lands lands under my control, I turn my attention on Hojo and Takeda. It is easy to keep them at bay until this point because Musashi is so easy to defend.

I find that sometimes it is good to take a step back and then leap forward 5. I approach many of the campaigns this way now, as oftentimes starting positions are tenuous at best.