Congratulations on your first elk.
For what it's worth,I shot an old cow with my muzzleloader and it was hot out, so I boned her out and put her in coolers asap. Figured the meat would be real tough after always leaving it on bone and not boning it out until time to process. It was surprisingly tender even more tender than the rag horn from this season. I think cows are better no matter the age than any bull.