I have a Hells Canyon edition, love it . I've owned three 7mm over the years,a Win. Model 70 , an A bolt Stainless Stalker, really like the caliber. I've hunted the 7mm caliber for 50 years, no complaints.
Personally I'd stay with a 7mm over 280ai , buying ammo is something to consider. 7mm ammunition is easily found anywhere, if you're in some small town with limited choices. Barrel length shouldn't be shorter than 26 inches in a 7mm ,if you want it to perform to its full potential, in my opinion.
All the calibers you have listed would be sufficient for elk, the 300 RM ,7 mm RM are fine calibers, but shot placement is the most critical. I'm 70 years old and have been blessed with much opportunity for elk hunting in my home state. I have taken many elk with a 270 and appreciate it for it...