I looked over this NASA report and it seems to me they didn't analyze for traces of organics any of the deep core samples. Is my assumption correct and if yes why wasn't this test considered?
They did, although apparently not on that particular sample and for the analysis that you link to, but the low carbon content was discouraging. No carbon, no organic compounds. Later studies of Apollo Lunar samples have provided some interesting, though perhaps expected results. It seems most of Lunar regolith organics that were found could have been imported to it via accretion of zodiacal (interplanetary) dust particles and meteor impacts.
From ALLOCHTHONOUS ADDITION OF METEORITIC ORGANICS TO THE LUNAR REGOLITH, Thomas-Keprta et al., 76th Annual Meteoritical Society Meeting, 2013 (PDF):
I'll let you read the rest of the paper from its source, but the analysis was done on same Apollo 17 samples as the ones in the paper that you're linking to in the question. I suspect there were many other tests for organics conducted on them, but this report should answer your question well enough. Apollo Lunar regolith samples were tested for presence of organics.