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I think you need the Node Queue module with the Smartqueue Per User.

Although it's not listed on the front page, you can now get the 6.x-2.x-dev version which does the multiple lists (or queues) per user.

I've also got a patch to make it work with the latest version of Node Queue.

This module might appear flaky because few sites use it and the issue queue is stale, but it really does work the way it's supposed to. We're using that 6.x-2.x-dev on a production site with premium content and it gives us NO problems whatsoever.