You definitely know IPA, so what I was saying is:
I've is supposed to be /aɪv/
The same goes for the other contractions, they just add /v/, and so are still monosyllabic.
Would've, according to that convention, would be /wədv/, but since it would be pronounced more like two syllables, /wədəv/, the contraction
would've is not part of the conventional ones.
That said, the way something is written doesn't force anyone to read it in a certain way. Just because it's written as "I have seen", doesn't mean I can't read it as "I've seen", or vice versa, so conventional contractions are just conventions that most native speakers don't need to understand or care about, other than learning them by heart in case they want to write according to some kind of "Standard Written English".
So I really don't think Americans ever say
I've to... /aɪv tə/.
If a reduced form were to be used, it would be
I have to pronounced as /aɪ ef tə/... more or less.
That's what I can say from my experience...