Use two HSAs and quit contributing to the spouse's HSA in Oct.
That way you can get the max contribution limits, and keep contributing to your HSA when your spouse can no longer contribute to his/hers.
HSAs have to be in each individual's names, even though spouses can pay medical expenses for each other.
The 2016 annual contribution limits are here: http://thefinancebuff.com/hsa-contribution-limits.html
But these are shown for a full year. You have to be eligible for all twelve months to contribut the full amount.
Since you have a family policy, the family limit applies to your total contribution between the two of you. But you will have to subtract the 3 months your spouse is no longer eligible.