Been there done that.
Super fun "hunt". (There's just a shitload of elk in there) . My advice is to take your time and enjoy the terrain that no one else ever gets to see. Its some beautiful country.
The 270 and 5 shell rule is definitely a fuddy rule. And its an old old rule.
When you consider that most of the oklahomans that get the hunt havent even seen an elk, or have only ever shot whitetails in woodlots and havent ever even shot at an animal in the expansive terrain (especially before rangefinders).... dudes were getting exciting and just lobbing rounds into herds of elk. Hence the rules. On my hunt we saw an old dude doing just that. 98% sure he hit one and we saw it lay down. But they didnt realize they hit it. One guy back at the campground brought a 338 lapua and was talking about missing a cow
On my hunt we got in there first (we saw like 40 cows but no decent bulls), the other hunters moved in and bumped some bulls over a hill and below us, we dropped into the pass and got great shot opportunities. Roughly 100 yards and 200 yards. Done by 3 pm the first day

.
The terrain is such that you COULD zing one a long ways, but its pretty broken terrain, you should be able to get within 300-400 yards pretty easy. My dad shot one just over 100 yards years ago. Mom shot her cow at like 200.
Nobody checked our guns. But had a 300 and 7 mag.
It'd be hard to argue against a 7 prc, especially if youre just gonna flip it after the hunt, but any medium round is fine.