Appreciate all the input and will know next time. Made several calls to others and they advised against going back up and gutting and quartering and just leave it as it was.
I'd start on the "inside" of the quarter that was up against the bone and trim away anything that's gray-ish. If there's not color difference, start taking thin cuts off around where the ball/socket joint was until the meat doesn't smell, then you'll know how "deep" to trim the rest. You'll figure out what the deal is w/the meat you've got.
I hope this next part doesn't sound harsh or sarcastic, it's not meant to.
Once you've got your meat managed, the next step is how not to let this happen again. Watch a few YouTube's or get a mentor that can show you how to quarter an animal "gutless", then, if you're able, get some OTC tags, offer to help friends who have tags left, or even shoot a few coyotes and practice.
Pretty much every critter on 4 legs give or take comes apart the same. Run a knife down the back from between the ears down to the tail and peel down towards the belly. Take the meat off side you've exposed, lay it on the hide, or put it in game bags, flip, repeat. Find where the short ribs are that contain the tenderloin, make a small slit and go in after them.
You don't need a hatchet or saw. You DO need a SHARP knife. If you don't have a knife that'll stay sharp through the process and you aren't confident you can touch it up in the field, get a replaceable blade knife and carry a few spares.
Unless you're in some super steep country or some kind of thick timber that doesn't allow for you to easily roll the carcass back and forth, with a little practice, a single person should be able to skin/quarter a deer/elk in 60-90min and 2 working on an animal it's 45min or less. Then you just need to decide if you're going to haul it, hide it (hide it from predators), or hang it until you can come back for the haul.