Here's mine, shot in Poland. I had him stuffed in Poland, and the shield - which I have gradually got used to - is hand-carved oak. That hunt was arranged by a chap called Pan Sikorski, but I know that he died some 15 years ago.
Regarding mouflon, it is worth keeping the fur - it is not so much wool - for any collars or other projects you might have a use for. The meat is also good eating.
Two years ago I shot a Barbary sheep on the Orange River near Kimberley. This was arranged and guided by a chap called Abrie Arlow who trades as
Pronk Hunting Safaris and specialises in exotic game in South Africa - exotic game being anything non-native. I suggest that he would well be worth chatting to. I see that he has some mouflon on his website, presumably shot in South Africa.
There seem to be two rates for hunting, one where the paperwork is in good order (which is needed to arrange the taxidermy and export of the trophy), and (the cheaper option) one without the requisite paperwork, which seems to be where the quarry has strayed over the border onto someone else's ground. On the basis that you would be able to salt the trophy, put it in a cooler, and dash for the Beit Bridge, getting any trophy stuffed in Zim., that might be an option for you.