I'm pretty sure 'great Ring' does refer to the One. But the statement from the Silmarillion doesn't have to contradict the Letter. The words 'took up' can be taken to mean that Sauron began using the Ring openly once again once he got back to Barad-dur.
-Voronwe
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"If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things." -- René Descartes
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