Yeah, FastQC is what prompted me to look at adapters in the first place. I get a big over-representation of 7-mers at 5' end of read, namely:
Sequence Count PValue Obs/Exp Max Max Obs/Exp Position
TGATCGG 4760 0.0 14.944738 1
TAGGGCA 10770 0.0 13.59925 1
TAGGGCG 5845 0.0 13.444971 1
TAGGGAC 7710 0.0 13.393038 1
TAGGGGA 7290 0.0 13.347217 1
TAGGGAG 10435 0.0 13.295226 1
TAGCGAG 3495 0.0 13.293988 1
TAGCGCG 3710 0.0 13.226308 1
TAGCGGC 4930 0.0 13.14511 1
TAGGGGC 9440 0.0 12.822517 1
TAGCGAC 3280 0.0 12.802791 1
TAGCGAA 2580 0.0 12.775723 1
TAGGGGG 7060 0.0 12.687389 1
TAGGGAA 8150 0.0 12.532882 1
TAGGCGA 2915 0.0 12.521299 1
TACGGCG 2205 0.0 12.457054 1
TAGGGCC 7555 0.0 12.361421 1
TAGCGGA 3060 0.0 12.35397 1
TTGGGCG 6700 0.0 12.340709 1
TAGGCAG 10400 0.0 12.229798 1
It seems that "TAGG" is quite a problem here. Not sure how to go from here though.