I've traveled up the Animas north of Durango, though I came in at Purgatory, and there's a trail on the opposing bank from the Durango -Silverton narrow gauge train at least to Needles. If you can't keep going north, then cut across Chicago Basin to Vallecito river, then go up to the CDT/CT junction and Highland Mary Lakes/Silverton.The train is not that much of an interruption, though they caught me washing up once - poor passengers. Trying to go east from Durango itself, then cutting north, there seems to be too much private property and roads, unless you want to hitch to the Vallecito/Florida reservoir area.
Add: I've checked out some public land on the west side of the highway from Silverton to Ouray, more looking for stealth car camps to sleep before hitting the Big Blue wilderness next to Ouray and (iirc) some forest roads run perpendicular from the highway into the forest with ridges and valleys everywhere. Didn't seem like many trails go all the way. Maybe the lizard head??