Two Glorfindels?

[Aiwendil]

The idea of reincarnation just seems to clash with the general feel of Middle Earth.

Well, Elvish reincarnation is very much a part of the Middle-earth mythology/theology, particularly the philisophically consistent version worked out in the 1950s. It is talked about at length in HoMe X, Morgoth's Ring. That Glorfindel of Gondolin and Glorfindel of Rivendell were the same person is pretty clearly established in HoMe XII, which Tirned Tinnu has just quoted.