The 6 month rule for Medicare is a good rule of thumb to avoid problems but is not strictly accurate.
Your "initial enrollment period" is the 7 months around your 65th birthday. If you enroll during your initial enrollment period, your Medicare starts either on the first day of the month that you turn 65, or up to 3 months later.
https://www.medicare.gov/basics/get-started-with-medicare/sign-up/when-does-medicare-coverage-start
If you enroll after turning 65 and outside your initial enrollment period, your coverage can start up to 6 months retroactively, making you retroactively ineligible to make HSA contributions.
But as long as your spouse enrolls when she turns 65, her coverage will start the first day of the month of her 65th birthday and you don't have to worry about a 6 month retroactive ineligible period.
