I just want to confirm that I need a Zimbabwe CITES export permit to bring home a Zimbabwe sport hunted elephant, but do not need a US CITES import permit.

The following was taken from the US Fish and Wildlife web page:

What permits do I need for African
elephant trophies taken in Botswana,
Namibia, South Africa, and Zimbabwe?
The populations of elephants from these
four countries are listed in Appendix II
to allow for trade in certain products
only, one of which is the noncommercial
export of personal sport-hunted trophies.
Thus, an import permit is not required
even though the African elephant is still
listed as threatened under the Act.

Correct, the CITES will be issued in Zim come from your operator in Zim and be included with your shipment to the States. For a leopard, you need the CITES issued on this end.