New here, found no mention of Plexamp, which uses date data from MusicBrainz.
Tried Plexamp’s 70s Radio, but found that a tune from Art Tatum Solo Masterpieces Vol 6 was included. Makes sense, since its earliest release date on MusicBrainz is 1977.
Would it be appropriate to edit to reflect the original date of 1956 (according to AllMusic)? If so, is there an FAQ related to this scenario?
No, you can’t just change the 1977 date to 1956 on that release. The date of 1977 will be from when that specific version was released to vinyl. It will have a different catalogue number.
To put the date of 1956 you will need to add a new Release for that original 1956 edition.
MusicBrainz is not a 100% complete history. So in some cases you will get a date of the earliest version that MusicBrainz currently knows about. This can often be the first CD release.
Paste some example links of the release you are referring to and we can help you fill in some gaps to point at the 1956 originals. 
Resources like Discogs and Wikipedia can help, but just like Wikipedia you need to be able to quote your sources.