Which species to raise?

Your very right not to want whitetail or mule deer in OK because you have lots of EHD there which will hit you every year with deer death.
I would do some research and find out which would not be effected by EHD and choose that animal. I would also check what harvest facilities want in your area. It would be much more enjoyable to raise something that has a better outcome from EHD exposure.

Elk I hear are resistant to EHD. I've heard Fallow are as well but there are lots of crap genetics out there and decent genetics are going for as much or more than a hunt so I can't see profitability. Pure breed rams of all species are high dollar. Jack could give more insight on that

Elk do seem to not get EHD very often but I have had one die from it in forty years. We have many with genetics of 500 to 600 typical antler frame. But out here in Montana we have to sell out of State as we have no harvest facilities due to a public vote on the harvesting of these animals behind our fence. Fair chase was what they expected for an on farm slaughter.
Elk that will be 400 inch's by four years old sell well and make some money. Calves or yearlings are the best way to go if you buy them in my opinion. Price on calves is 1500 to 2000 with yearlings at about 500 to 800 more of the calf price.
Hybrid sheep have never had EHD on my place even when they lost 90 plus percent of wild whitetail all around me from it. We raise bighorn and stone sheep hybrids. We do raise 50 to 100 lambs a year and sell almost all of them each year. Price on lambs is 1500 to 3500 just depends on lamb genetics.
This ram was sold into Texas and then sold to a harvest facility in Nb. Ram was born on my ranch from my genetics.

Jack what is the end game with the sheep? Hunts? Meat? Are they high percentage big horn or a mouflon type cross ? Interesting

I sell the sheep if lambs for breeders and adult rams for the harvest market.
North American sheep have no immune system for pneumonia and have only one lamb and are slow in horn growth.
My idea was to get twins for better production and better body size in rams. Our rams will weigh from 250 to 300 pounds so are very impressive. Horns will be 35 to 40 plus inch's with 14 to 15 inch bases. We also got better horn growth in rocky mountain bighorn hybrids and they will be almost full curl at 3 1/2 years old. Big rams like this I get 6000 too 15000 just to give an idea of their worth to harvest facilities.