I can’t picture “Foot short of lining up with the living room”. Sounds like you are missing a few square feet of the new flooring? And you’re trying to figure out where the gap goes?
cut that foot wide piece and have it connected to the living room or should cut that to go under the sink base
I can’t make sense of this. Partially because ‘cut’ makes it sound like you are working with large sheets of flooring, not t&g. But also because of course you’re not gonna waste flooring under a cabinet when you don’t have enough so I must be misunderstanding you.