"Can I open an HSA with a third party, carry a High Deductible plan through my employer, and have Medicare pick up some of my wife's medical expenses?"
Yes. As long as you are covered solely by the HSA compatible HDHP, you can have as many HSAs in YOUR name as you like and contribute to any or all of them where the aggregate total contribution is within the limit amount.
Your spouse cannot make contributions to a HSA in HER name because her Medicare enrollment prohibits it..
