Did some camping in beautiful Tinajani Canyon near Ayaviri, Peru. Judging from what I saw, one could take a colectivo (small bus) from Ayaviri, up the canyon and camp somewhere, then take a couple days to paddle out to Highway 3S and pick up another colectivo to head into town. There’s a little “campground” in the canyon where you could ask around and get your bearings. Coordinates are -15.016498, -70.580499. Rainy season would be better, as I’m told there’s little water in the dry season. Didn’t see any rapids from the road, but couldn’t scout the whole thing.
Note: this is just a quick little possibility, I haven’t done it myself. But if you happen to be in Peru with a packraft, and you’re doing the Puno to Cusco tourist thing, this could be a fun little side trip. The canyon has many secrets to find if you care to get out of your boat and hike around.