There is a herd of chamois in a private facility in Texas, but they are not on exhibit to the public. They've expressed interest in acquiring our chamois, but ruminants are not allowed into the US at the moment, which makes it rather difficult!
The oryx are in a similar boat, but nobody is especially interested in taking them - both animals are quite old, and the male has been neutered. And since they are an SSP animal, there are several more hoops to jump through than might be otherwise. The zoo has committed to housing them until they die.
This past year was tough on our wisent - two of the three died, leaving a single old female. Right now, she is living with a small group of wood bison that are new to the zoo.
Eventually, I believe the Barbary apes are going to be phased out (when they start construction on the new Eurasia), as are the tur. Nothing is ever concrete in the collection planning process ... for most of the animals mentioned above, think of "phase out" species as those which are intentionally not allowed to breed in order to prevent the population from growing (and allowing it to shrink with deaths).