A very limited number of Marriott hotels list Encore rates under NPR, often alongside Entertainment Card rates.

A (semi-functional) web site promoting the Encore/Preferred Traveller program can be accessed at www.virtual-encore.com
Not sure whether Encore really exists (the web site certainly raises questions) but if booking these rates or any others requiring proof of eligibility, one should be prepared to produce a membership card at check-in.

FYI - Of six Entertainment Card reservations this year, I was asked to show a card three times.