Well...
The Amur, Malayan and Sumatran tiger populations in US zoos are pure, as are Amur leopards. Zoomix tigers are usually relegated to ZAA/other non-AZA facilities (though there are Amur tiger populations within ZAA/other non-AZA facilities), and Amur leopards getting all the holders they'd need for a genetically viable population is the way to go, though *a* tropical leopard species would be nice for Southern US zoos. (Sri Lankan leopards would be amazing IMO)
Asiatic lions haven't been a priority for a while, though I agree there actually is value in the EEP collaborating with AZA zoos to expand their Asiatic lion breeding programs.
To answer your question fully, it probably isn't worth the effort to do so, and AZA facilities are better off working with EAZA or other internationally accredited facilities on endangered big cat programs. Topeka Zoo and Oklahoma City Zoo each sent Sumatran tigers to Auckland Zoo, and I believe Point Defiance Zoo imported a Sumatran tiger from Taronga Zoo that stopped over in Memphis, though I could be wrong on that.