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Maybe a Kobo and install Koreader would suit you best. The combo ticks most of your boxes. You have to register, but it's just an email address. Don't know about syncing. I know Koreader has syncing options. Be warned, it involves installing patches and add on programs to your Kobo. I have Koreader on a Kindle and it works very well, but it's a lot more complicated than a Kindle.
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