I would charge $500 to clean it and go buy them another. If you enjoy the challenge, great, but these usually take so much time and the results are so poor that you may as well call them disposable.
It's possible to wet the rug out evenly and work on the spots, but you're unlikely to be successful at removing the spots without altering the color in those areas. The bad things that could happen are uneven color loss, even if wet out evenly, and water marks if it dries unevenly. This type of rug really needs to be tacked out during cleaning to stop shrinking and curling. In this case the binding has already shrunk and is screwing up the corners.
PS: They make a fantastic biodegradable weedblocker.