Can about guarantee if you call Josh at Trails west and tell him what tag you have, he will go above and beyond to get you on a hunt. He has access to hunt many of the best areas around the Cody region. Both units you listed he hunts, along with others. You can talk to him about what time/and how much time you can take etc, and he can list out the best plan for unit to hunt etc. . I personally dont know Josh, i just know of him and he is highly respected in the outfitting circle for running a top notch operation. I know a couple of the guys at South Fork outfitters, and they definitely will go above and beyond as well, but they are pretty well focused on the 1 late area. . Boulder basin outfitters is also well known for the late tag as well.
I will say, i have hunted the late tags, and it can be incredible. Seeing hundreds of elk a day, and choosing your bull basically. BUT, every year is different. Last year was the hardest ive heard of for late tags. I knew people who had both areas you listed, and they never saw much for elk the entire season due to lack of snow. But, that is why going with an outfitter who can work with you etc, will only benefit this once in a lifetime chance for you.