One of the places is the only US holder of three-striped palm civet, one of the first two holders of pale fox, and one of the first holders of Geoffroy's cat. They also have brush-tailed.
Another is North Georgia Wildlife Park. I can't find a photo, but they do have some less common small mammals.
And here's the third:
Log into Facebook | Facebook
The Eastern/Tasmanian would be at Tennessee Safari Park, which I do find unlikely.
As for Woylie, feel free to add anywhere I'm missing from my rough list:
Animal Edventures
Animal Wonders Inc
Birmingham Zoo
Bridges For Brain Injury
Capron Park Zoo
Cleveland Metroparks Zoo
Columbus Zoo
Cub Creek Science Camp
Darby Acres Farm/Safari*
Frankin Drive-Thru Safari*
Gladys Porter Zoo
Lake Superior Zoo
Lincoln Park Zoo
Los Angeles Zoo
Oak Creek Zoological Conservatory
Pacific Animal Productions
Potawatomi Zoo
Prospect Park Zoo
San Diego Zoo, Safari Park?
Smithsonian National Zoo
Wildlife Encounter Ecology Center
Wildlife World Zoo
Wowee Wildlife
Asterisks are unconfirmed.