Alot of great posts. Most everyone seems to have agreed that there is no direct Buddhist influence in the Legendarium and any resmeblances are due to the universality of many of the facets of Truth.
Several times folks have made statements to the effect of Buddhism believes _______.
But a crucial point is I think being missed. No religion has changed so much from it's inception [with the likely exception of Protestant Chrtistianity]. As 2 of the branches or Vehicles as they are often translated, of Buddhism has. At least from my studies and talks w/ Buddhists. The Buddha originally refused to speak to re-incarnation, existence or permanence of the soul and several other points that Mahayana [incuding Zen] and Vajrayana [primarily TIbetan B.] have dogmatized.
So to speak of Buddhism as monolithic makes it difficult to discuss specifics in Tolkien [or Buddhism for that matter

]
My readings on Buddhism are a decade or so old, so I may be off...
One does find many sources for Tolkien's writings, he never to my mind tried to hide them.
He digested virtually the entirety of Northern European Mythology and Roman Catholic CHristianity and gave it back to the world both new and improved and, an "Older Testament" if you will.
But I see no more hint of Buddhism than of Zorastrianism or Shintoism.