I've got to admit, I always get a headache when grammatical terminology is bandied around as if it explains rather than merely describes a fact of our linguistic practice.

In most of the examples you offer I can see no possible confusion ~ eg, "i've got a headache" = "I have (possess) a headache"; "I've got to go" = "I must (am obliged) to go", and so on.

But doubtless I am being a mere clown and have misunderestimificated your confusionisation... :)