I was in a similar conundrum when I drew my OIL tag last year. My only rifle was a 6.5 CM that I shoot well. I have some buddies who are Afghanistan war vets, they get opportunities to hunt oryx often through vet programs and have taken 10+, all with a 6.5 shooting 143gr ELDX at varying distances up to 475 yards. They all told me I’d be fine, so I started working up loads for my rifle. But eventually I decided a OIL tag was a good excuse to buy another rifle and coupled with the fear of making a bad shot and wishing I had more gun/energy behind my bullet. I bought a 300Win and worked up loads shooting 180gr. TTSX bullets.
Fast forward to last month and I shot a cow at 125 yards with the .300 Win. My shot was little behind, clipping both lungs and missing the heart and shoulders. The cow dropped with yards of where I shot her. At 125 yards my bullet traveled at 2858fps and delivered 3265 ft-lbs of energy. That had to make a difference.
Later that day when I dropped the skull at my taxidermist he was surprised at how my shot went down. He had been on a hunt where his buddy made a perfectly placed shot at 300 yards with a .300 win, and they had to chase that oryx down and shoot 6 more times before it died.
Moral of the story? If you can swing it, buy a bigger caliber. If not you’ll likely be fine with the 6.5 but focus on that shot placement and don’t be tempted to make a rushed shot.