USAGE: Haves and have gots

I'm not so sure about the idea that 'have' will become 'got', especially
'will got' < 'will have'...

    I'll have someone do my taxes.  ==
    I'll get someone -to do my taxes.

["I'll have someone -to do my taxes" to me implies more like the
math-challenged groom thinking of the benefits of future life with his bride
than hiring some kind of accountant... unless of course the bride _is_ the
accountant]

    *I'll get someone do my taxes ?

(Or not.)

I just caught myself saying "I got some listed on my website..." but the
future of that would be "I'll get some listed" (I'll put them there) and I'm
not sure it'd be "I'll have some listed" unless someone else wrote my
webpages.

Now... are there places where we've got 'have' and can't have 'got' or 'have
got'?
Someone mentioned 'have to' as in "hafta go" but even there we have 'got to'
("gotta go")...  but:

    I have sandwiches every day for lunch.    [I eat them]
    I've got sandwiches every day for lunch.  [They're put in my box]
    I've gotten sandwiches every day for lunch.  [Before they run out]
    I got sandwiches every day for lunch.     [Talked her out of corn dogs]

So I don't think 'have' in the sense 'to eat' can be so replaced.  (You
can't eat your cake and have it, too?)

    I have learned much.
    *I've got learned much.
    *I've gotten learned much.
    *I got learned much.

Those last three will have the grammar teachers beating their students for
misuse of 'learn'.  ("That'll learn ya!")  But 'have' as auxiliary (?)
stays.  (Except maybe in 'I have done'/'I got done with', any similar?)

    I have homework.        [Gotta study it.]
    I've got homework.      [Gotta study it.]
    I've gotten homework.   [Been given to me.]
    I got homework.         [Gotta study it.]

"'ve gotten" is the only different one (but you've discussed this already).

Um.. that's too much for me; I'll shut up now.  (Having fun, yes, but not
getting any--erm, wait)

    *Muke! (who never ceases learning things here..)