We decided to try improving things by running them through TrimGalore! to remove adapters and poor quality sequences.
Processed the samples on Roadrunner (Apple Xserve; Ubuntu 16.04) using default TrimGalore! settings.
After trimming, TrimGalore! output was summarized using MultiQC. Trimmed FastQ files were then analyzed with FastQC and followed up with MultiQC.
Documented in Jupyter Notebook (see below).
Jupyter Notebook (GitHub):