[1]http://articles.latimes.com/.../news/ss-570_1_4th-century-ad

  The earliest full copy of the psalms dates from the 4th century.

  it is in Coptic. Not Hebrew. .

  The Interpretation espoused by Theodore of Mopsuestia also dates
  from the 4th century AD.

  While Mopsuestria was in a different area; not Coptic,
  nevertheless, considering this was a period of time where
  establishing defacto standards for what belongs and what doesn't
  belong, it's likely that Theodore's text in his language was
  functionally identical to the earliest surviving Psalms.

  This to me, would mean if the earliest physical source material
  is dated in the same era as the first interpreter of the Psalm
  that I can find...

  ...his interpretation would be likely the closest to proper.

  Now, this can be wrong. I'm searching for earliest archeological
  evidence of Psalm 137. Maybe something in Greek. Maybe Latin.
  Maybe Hebrew.

  So far, can't.

  So far, it's Coptic. Now the Septuagint; the first complete
  Septuagint and New Testament is from 450 AD
  [2]https://en.wikipedia.org/wiki/Codex_Alexandrinus
  So even if you don't like the Coptic from the 4th Century as the
  complete Psalms, you can have the whole thing about 70 years
  later.

  Still a lot closer than ... oh.. .let's see... when we are
  today... interpreting it from our perspective in the 21st
  century.. rather than theirs in the 4th and 5th centuries.

  21 - 5 = 16 centuries.
  21 - 4 = 17 centuries.

  Whose interpretation is closer to potentially being accurate?

References

  Visible links
  1. http://articles.latimes.com/1988-12-24/news/ss-570_1_4th-century-ad
  2. https://en.wikipedia.org/wiki/Codex_Alexandrinus