LJ does have a good point. Especially since I am looking at the updated pictures where the leaks have been noted.
The clog might not be post cleanout, it may be just above it.
One option, cut the pipe above the cleanout, remove the cleanout from the line (since you already have a joint or two below that will allow it's removal) and check for a clog by looking through the pipe with a flashlight. You can reassemble with another one of the clamp type joints and rotate the cleanout to where it's easier to access.
Another option (one I've had to do before) is to run the snake from the roof vent to the cleanout location. You can remove the section of pipe below the cleanout and replace with a bucket, then run the snake down from the roof. If it's a straight shot, you might be able to see if there's a clog by shinin a big a$$ light down the pipe.