I understand this completely, and share many of the same feelings with you, but here is the deal. Who do you want to stay anonymous from? If it is from a government or big corporation, then that is quite tough, but not impossible. You mainly would have to use all the privacy tools at your disposal (especially tor) and use several personas to post stuff, encrypt everything and try to impersonate them as much as you can. And remember the more intricate a persona "history" is the more difficult it will be for you not to get attached to it, and the more time you spend with a persona I think it is easier for your personality to "seep" through the cracks.
If you just want to stay anonymous from the general public, then don't fret too much, most will never make a connection between different handles.
Now here is the fun part, I think all of us have a public face and it is even good to show it around a bit, then you can create personas to do all the other stuff you want, and kind of compartimentalize your activities online, this way you through a lot of people of the scent of your real self.
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