The Western Rim trail was always on my list but I never got around to doing it. I think it would be one of the best higher elevation rides in the area (snow until early July). There is one short section that the Forest Service map shows as being in the wilderness (around Benjamin Spring) but that could be wrong because it also shows a double-track running through it. All other sections of the trail that go through the wilderness have a double-track work-around. You can start as far south as McGraw Lookout and follow double-track along the rim. The double-track tends to be primitive throughout this general area. Use satellite imagery to see if areas through old fires have trees across the route. That area just north of Warnock Corral may be a grey area when it comes to wilderness. In any case, enforcement is nearly non-existent. You can go as far north as Lord Flat but don't try going further north down that trail to the Imnaha River! Good way to die. Just backtrack and take the Hat Point Road down to Imnaha.
The route from the community of Imnaha, down the Imnaha River road, and then the last 6 miles down the Imnaha River trail is quite nice, except during the summer when it is hot as hell. May is best. You can extend this into a challenging loop back to Joseph (
https://ridewithgps.com/routes/13374778) but it is a wild adventure. Highly recommended though. The best I've done in the area. Again, a May trip. (
https://wordpress.com/post/obscurus11.wordpress.com/1226)
The only ways to access the Snake River on the Oregon side is the Imnaha River road (skip the Dug Bar option, it is not that interesting), Jim Creek (although I heard this trail has now disappeared), or Cache Creek. I've never been down Cache Creek but I've heard it is interesting and passible. Jim Creek and Cache Creek would be out and back routes.
I haven't heard of the Lake Fork Creek Trail -- what is it near?
The Wallowa River offers only paved and gravel roads through ranchland in the valley. Upstream of Wallowa Lake is wilderness. There is a route from Wallowa Lake along dirt roads southeastward to Salt Creek Summit and beyond that is quite pleasant. More of July or August trip. This can be combined with a circumnavigation of the Eagle Cap Wilderness if you really want to get crazy (I probably won't do it again).
Let me know if you want advice about any other options.