Can you contract the main verb '[I] have' in a sentence?

One can contract I have to I've when have is a helping verb, e.g.

I've got an octopus in my pants.

Is contracting the main verb technically incorrect or merely antiquated? My father loves to say,

I've a month-old smoked shoulder I can cook for dinner,

and he sounds like a crazy old man when he does. I would like to know if I can shut him down by informing him that he is incorrect. :)

Contracting the main verb in a sentence is perfectly fine. It sounds awkward only when the pattern of prosodic stress falls on that word:

I have to do it.
* I've to do it.
I have yet to do it.
I've yet to do it.

But this is probably just because you can't use a contracted form in a grammatically stressed position, such as:

I don't know what it is.
* I don't know what it's.

But even then, there are sentences in which the stress falls on the contracted word and it doesn't sound awkward, showing that it's not ungrammatical except perhaps by the standards of a mad prescriptivist somewhere.

In American English, the contracted form ’ve is only possible as an auxiliary verb. It is not grammatical as a main verb. This is not the case in British English, where it is grammatical, and this is one of the differences between British and American English

Yes.

I'd not even consider it antiquated. The contraction that is - the shoulder's a different matter.