Thanks guys.

I decided to apply for the Marriott Premium Visa Signature card using the link at FreeFrequentFlyerMiles.com, credit card, free cards (I don't see a way to link to this page).

$65 gets you 50K points, a free up-to-Cat. 4 night, and a free night (seems limited to Cat. 5) on your anniversary. First year $65 fee is not waived, but seems worth it in my situation. You only need a one-time charge, so I should get the points on my first cc statement.

In case something goes wrong -- like Chase is being picky with apps -- I can combine points with my wife and reach the 35,000 I need. And Marriott is helpfully allowing me to make the award rez even though I don't have enough points yet in my account.