You can do the full $8200.
IRS 2008-59, Q&A#16:
Q-16. How do the maximum annual HSA contribution limits apply to an eligible individual with family HDHP coverage for the entire year if the family HDHP covers spouses or dependent children who also have coverage by a non-HDHP, Medicare, or Medicaid?
A-16. The eligible individual may contribute the § 223(b)(2)(B) statutory maximum for family coverage. Other coverage of dependent children or spouses does not affect the individual’s contribution limit, except that if the spouse is not an otherwise eligible individual, no part of the HSA contribution can be allocated to the spouse.
https://www.irs.gov/irb/2008-29_IRB#NOT-2008-59
