Wow!
First of all, the only areas north of Cody for general license are 50 and 52. 56 also, but is west and south. You need to be careful about some of that area because a lot of it is wilderness and non residents can't hunt wilderness without a licenced resident, or an outfitter. Sucks, I know.
Doesn't look like a lot of it is in Nat'l forrest either.
Looks like there's quite a bit of BLM, but who knows where you should go.
If your buddy in Cody has to work, at least he might be able to tell you where to go and have maps.
An outside shot would be to call the Game&Fish main office and find out the name and number of a Cody game warden or biologist. They might be able to help.
Call the Chamber in Cody, talk to Gene Bryant, and see if there are any lists of local landowners willing to let you hunt. The land owners might charge a "tresspassing fee", but could be a better guarantee for less than an outfitter.