the light that we are currently observing emanated
  from an object that was only 13Gly away

Using http://www.astro.ucla.edu/~wright/CosmoCalc.html, the light of an object at redshift z=8.68 was emitted 13.141 Gyr ago, 0.579 Gyr after the Big Bang. The co-moving distance (to where that object was) is 30.444 Gly, but at the time the light was emitted, it was only 3.145 Gly away (=30.444 Gly/(1+8.68)).

  we cannot see past 13Gly because the light has not
  arrived, and this is patently TRUE

We should be able to detect light from Population III stars, i.e., redshifts between z=20 and z=100, so about 13.540-13.704 Gyr in the past (about 0.016-0.180 Gyr since the Big Bang) and at a co-moving distance of about 35.851-42.045 Gly (or distances from us in the past of 0.416-1.707 Gly).

Edited to add: For more information, refer to https://en.wikipedia.org/wiki/Scale_factor_%28cosmology%29, specifically the FLRW metric, https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr....