Nilgai would be my choice if the travel and cost isn’t an issue.
Nilgai is a great idea, very wild to hunt and amazing to eatAlso consider a Nilgai hunt in south Texas. Great meat, short hunt and easy to do.
Took a look at your website. Absolutely stunning Ranch and Lodge.I occasionally offer management hunts for a variety of species. Currently offering broken horn Scimitar Oryx Bulls at $3750 for 2 days all in - guide, luxury accommodations, meals and open bar. A few have only one broken so you could mount as is or have taxidermist repair plus outstanding table fare. Will offer some Red Deer hinds this Fall as well.