@Opus 17
"then the wife is also deemed to be covered by a family HDHP." Yes, the spouse was covered by a Family plan for those three months (if the reporting on which months is accurate, as you point out); however, we are talking about the calculation of the annual HSA contribution limit for each HSA here.
The annual limit for the Family coverage is $7,000, to be shared between the spouses. In the calculation above, the entire $591.66 (one month Family coverage) is allocated to the husband, so you also can't allocate it to the spouse for the same months.
However, because of the last month rule, the spouse can claim $295.83 for each month, regardless of the shared Family coverage. Hence the spouse has $3,550 for the annual HSA contribution limit while the husband has $4,438, which is 9 months at the Self-only rate (thanks to the last month-rule for the husband - remember, on December 1st, he had changed to Self-only) plus three months at the Family rate.
I chose to allocate the entire Family coverage for those three months to the husband, because that minimized the amount of excess by the husband.
"The wife is allowed to have an HSA " - I missed the heading - "or my own HSA and my wife's HSA?", so she did have an HSA all along, so anything I said about her opening one is moot.
"the taxpayer needs to indicate that the wife had family HDHP coverage for September, October, and November." - I am sure the taxpayer did enter that, or else the excess calculations would not have turned out as they did.
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