I think you are playing with fire to leave Shimazu unmolested. As Asai has stated, clans have a tendency to be somewhat dormant for a time and then explode across the map. Shimazu is one of those clans, especially after he starts training Nodachi. And he has not one, but two emissaries in Iyo

And they are in, what I call the "hunkered down" position which means they aren't going anywhere anytime soon. In my experience, that is the prelude to invasion, as the AI likes to opt for "cheap spies" that bypass local security. It might come soon, or it might not, but the AI is definitely looking in that direction.
That rebel garrison in Hizen looks formidable...the Mori garrison in Iyo looks much more vulnerable

And he appears to already have NC, which will not be fun to defend against in the rolling, non-forested, terrain of Iyo, and also means his infrastructure is getting well developed...ie--he has a sword dojo and a famous horse dojo, somewhere.
My fear would be to continue to stretch north, only to have the "Green Horde" come knocking at your southern flank. Several Kyushu provinces would yield as tidy an income as any in central Japan. Chikuzen, Chikugo, and Hizen all have a base farm income above 300, and would yield well with an upgrade or two.
I realize this is probably the "ho-hum" boring way, but you have to fight Shimazu at some point----his only way to expand is through you. Better to do it before he gets developed, IMHO. Rather than eliminate Oda, I'd keep him as a buffer against whoever comes south from the Kanto. A rather temporary buffer, to be sure, as an AI-led Oda rarely can hold up to Takeda or Hojo.....but I've seen it happen, just the same.
Just my 2koku...............