I saw the "rare" 1963 version listed at
[archive.org link to sophiararebooks] for $4500.
(I was going to post the original link, but it was just taken down by the bookseller because he realized,
in my response to my query about it, it had already been sold. For archival purposes, I'm glad that archive.org had a copy. )
I learned that this particular item was just the first 11 lectures (at 155 pages) printed in 1963 [with no mention of 1971 on the cover sheet].
Sadly, my version is the 1971 version, with the additional 5 lectures (at about 228 pages).
The cover page adds has a line referencing 1971.
I had bought mine a while ago (in the late80s/early90s) when I visited the CalTech bookstore.
This is the version that what was corrected, re-typeset, and republished by Preskill.
No luck in my search through numerous university library sites.
If there is a copy in some library, it shouldn't have a publication date of 1971 or later.
If it has a 1963 publication date or if listed as "unpublished", it should have much more than 155 pages (and more than 228 pages).
So, I suspect that there are two 1963 versions...
one with just the first 11 chapters [like the one above], and rare more complete set of 27 (with more than 300 pages, I would guess).
(Maybe those last 11 lectures are only in handwritten form or partially-typed form. Maybe audio? [see the Warsaw reference below])
Here are some references to what Feynman was thinking about on quantum gravity:
(1957) Feynman's "Critical Comments" at the 1957 Chapel Hill conference:
http://www.edition-open-sources.org/sources/5/32/index.html
(1962) Here is someone's scan of journal article of Feynman's "Quantum Theory of Gravitation" in Acta Physica Polonica
http://blogs.umass.edu/grqft/files/2014/11/Feynman-gravitation.pdf (from the 1962 Warsaw conference)
(1972) Here is a Google Books link to Feynman's
"Problems in Quantizing the Gravitational Field, and the Massless Yang–Mills Field" (reprinted in "Selected Papers" edited by Brown, originally from "Magic without Magic" edited by Klauder)