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The following is from The American Heritage Book of English Usage from Section 144. "got/gotten":
"In American English, have got is chiefly an intensive form of have in its senses of possession and obligation and can only be used in the present tense."
To use "had got" for reported speech seems ok, but to me as a native speaker it looks and sounds strange. Also, it's not possible to use it for a simple past sentence. For example, I can't say "Yesterday I'd got money"; I have to say "Yesterday I had money."
As an English teacher in Spain I no longer teach "have got" in any context, except to make students aware of it's usage or unless a student specifically asks. There are three reasons for this:
1) As mentioned above, "to have got" is only really applicable to the simple present tense, whereas "to have" is applicable in all tenses.
2) According to my understanding "have got" is only common in British English and is not used at all in the U.S. (I am not sure of it's usage in other English-speaking countries).
3) To me as a British English-speaker "Do you have...?" sounds more polite than "Have you got...?" without being excessively formal. Actually, it sounds more "educated".
The verb "to have" is therefore more universal, simpler for students to assimilate and it makes their English sound better.
I certainly don't recommend that you use "to have got" in the past tense. What I would recommend is that you mention it only as an aside and focus your attention on the verb "to have".