Your data have very high levels of duplication and in the 10,000+ region. That is quite worrisome. In RNA-Seq duplication levels in the tens and hundreds are ok, 10K+ region is not ok. Your most duplicated sequence:
CTTCGATGTCGGCTCTTCCTATCATTGTGAAGCAGAATTCACCAAGCGTT
is present 200K times and appears to match ribosomal DNA.
Hence to me it looks like your data has not been rRNA depleted most of the reads will map to rRNA. You may have to make do with just 7% of the data meaning about 2 million reads from the original 39 million. That may or may not be sufficient.
At this point worrying about quality filtering or kmer content is not all that relevant, that won't really make much difference.
This looks like an example case for What is the reason for most software errors in Bioinformatics according to you?