""Young and tender" didn't become a cliche by accident. However, with proper field-dressing and a quick cool-down and then knowledgeable butchering, it's all good eating."
Agreed - in spades (to a point)
I've yet to see any "bad" elk - no matter the age or size.
First things first. Take care of the meat in the feild right away & there is no bad elk.
Get the thing gutted ASAP - tremedous amount of heat inside that big ol' thang.
Always think COOL(er the better) & DRY. Elk's hide helps to retain body heat - strip it off as soon as possible to allow the meat to cool off. Too, that'll allow a "film" to form over the meat which helps protect it from bugs, moister loss & other nasty stuff. Hang it so it can get unobstructed air-flow around it (more cooling), hang a tarp so it shades the meat all day but doesn't touch - you want great, unobstructed air-flow & the cooler the better - & right now. We've hung elk quarters at 50 degF+ for 3+ days (daytime temps (night times going to below freezing) not recommended, BTW) in total shade & good air-flow withg zip for bad meat. I think that's pushing it .... AZ ought to have similar humidity as CO which helps regards forming the "skin" & not radiating the heat all over as with more south eastern areas. Cheesecloth won't keep flies from laying eggs in the meat unless it's hung a couple inches away from the meat - you may have to rig a "mosquito net" to keep 'em off.
If you have to due to the weather, get that thing out of your hunting area ASAP & into a cool(er) spot. Leave yer buds & get the meat in a cooler - you may prepare with a coupla big(ger) size coolers for this very reason - never hurts to have 'em on hand.
Bone your meat. Cuts down on cooling time, makes it easier to pack out of the woods (don't think I'll ever pack any bones out again) , & stores easier at camp if in coolers. Besides, you'll (or the processor) end up boning it out away for the best freezer storage. Quarter & slice up the length of the bone & then just work your knife along the bone to get as much meat as possible in one great big hunk. Wrap (cloth-type stuff, not plastic) & pack out.
Be prepared for some real work gutting, skinning & boing. A smallish/yearling cow elk can go 300 pounds & even rolling one over by yourself can be a chore - & doing so on a hillside just adds to the "fun."
they tend to slide for every rollover. At least a couple 20'+ lengths of decent rope helps anchor the darned things before rolling. The standard 550 parachute cord is certainly strong enough, but seems "skinny" to me. I use a couple 1/2" wide tubular straps (came off a F4 drag chute). Still a couple hanks of 550 chute cord's always handy to have & you will want to have something to hang the stuff you can't pack out - 'chute cored works great for this. DO split the brisket & prop open with a stick or two - aids cooling, but if you quarter quickly, no need as the bulk of the biggest meat is isolated from the body.
You don't need an axe, an Arkansas Toothpick, or even a saw to do an elk. I use a lockblade Swiss Army knife as my primary & a cheap-O Western/Coleman "skinner" to peel the skin & for anything "real heavy." With some anatomy know-how, you can do an entire elk with a 2" blade. (no, I haven't, but you can. You certainly don't need 10 pounds of knives & saws .... )
Take a garbage bag (yep plastic) to take out the tenderloins & backstraps (perhaps 35+ pounds of prime meat) immediately in your daypack - you'll be back soon enough with bigger/better tools to cart out the remainder.
BTW, anytime you can, always shoot one so you only have to carry it's pieces parts downhill. Lugging elk parts uphill sucks. Better, shoot one in camp & close by the truck.
All told, for an "any elk" tag, I shoot the biggest one I could - just adds to the quantity of the meat. & about that "no dead critters hanging on the wall" bit - saw the antlers off at the skull & you will find some use for 'em - sometime.