If you say “That’s all I have to say” does “have” mean possess or need?
“That’s all the words I possess in my arsenal to contribute to this conversation” versus “That’s the extent of my need to speak”?
Secondary question: Would anyone else change the pronunciation of “have” depending on which meaning you intend?
For me, yes. Absolutely.
“That’s all I hafta say” = “That is all I’m required to say.”
Both my wife and I agree
“haff to say” means I’m not required to say any more.
“have to say” means I’ve spoken my peace.
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For me, yes. Absolutely.
“That’s all I hafta say” = “That is all I’m required to say.”
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Agreed, although I can’t remember ever uttering the words in that sense. The other sense would seem more likely to crop up in real life.
But does speaking your piece mean as if from a compulsion, like “I just gotta say this thing. Now, I’ve said it and I’m done”? Or is it, “I have run out of words. Those were all of the words I had”?
For me: “Those are all the words in my possession that I have any intention of uttering right now in this context.”
There’s no compulsion, or it would be pronounced the other way.
The ambiguity disappears when you use the expression differently. For example, I have something to say. Pronunciation shouldn’t vary and, in any case, will depend on the speaker’s region.
“don’t have to” very often means “don’t need to”.
NM… I just repeating “have to”= “need to” Vs “have”= “possess”.
It can mean a lot of different things, depending on where you put the stress:
THAT’S all I have to say = “That last thing I just said? That’s the key to what I mean.”
That’s ALL I have to say = “I’m done talking on this topic now, having probably said quite a lot.”
That’s all I have to say = “Someone else may have a different, much stupider, opinion.”
That’s all I HAVE to say = “I’m taking the Fifth.”
That’s all I have to SAY = “Time for action!”
Additionally, context can add still more nuance. English is not like a sequence of programming statements, each statement rarely has a complete and precise meaning all by its lonesome, it depends for its precise meaning on context and (in the case of the spoken language) intonation (sarcasm, fervor, doubt, questioning, assertive) and stress.
Depends on whether or not I’m testifying. 
I would add: “That’s all I have to say” = “That’s all I MUST say,” and anything additional is up to me . . . as in “name, rank, serial number.”