It is a very pretty area. Not as big, wild and spectacular as the Sawtooths but cool none the less. I'm assuming when you say Medicine Bow that you mean the NF by that name and I'm guessing that you would be working somewhere in the Snowy Range, west of Laramie? And you're right, no grizzlies there. You would have closer access to "civilization" at Laramie, Fort Collins and the Denver/Boulder area if you need it.
The Greys River area is cool and quite remote in terms of access to the fruits of civilization. I'm guessing you're right about griz being in there. I drove the length of the river many years ago, spending about 5 days in there with my family and remote is the operative word.
Don't know much about Cour D Alene other than I've been through there a few times-Big Lake/Lots of trees.
If you do go to Medicine Bow let me know. It's about 2 hrs from where I live. Maybe we'd have a chance to get together for a hike or a beer!
Hope it works out for you.