You are going to some of the most beautiful and remote country in -- the country -- and for damned sure in Oregon. You will run out of time long before you run out of places to explore and enjoy.
As you know, travel is slow, and distances are far out there, and depending on the weather in May, -- well, I've seen it when a lot of travel wasn't hardly possible. Generally you'll be OK, but too much rain can be a game changer.
I personally hate to see folks kill the coyotes out of fur season, as those little critters are a valuable resource for a lot of folks who have pretty lean incomes in a area that is hard to make a living at best. Depending on the year, jack rabbits are usually plentiful enough to provide sport for a guys "blood thirsty" moments.
I haven't been over there for awhile, but the spring-time rafting industry was getting pretty popular on the Owyhee, and the Three Forks area was seeing an influx of those folks at this time of year. After the water goes down, they're done.
I based most of my activities in the Rome area, calling coyotes, deer hunting, and in general burning lots of gas. Three Forks Hot Spring is very cool, and the branches of the river have great small mouth fishing.
This thread brings back many fond memories, and I'ma hafta find my pitchers.

jd