Suddenly the light went on: printing is a QTR function, nozzle check is an Epson function.
Any pinkish hue I may have seen in my very first piezo prints were caused by PFlush remnants in the ink lines. The nozzle check test pattern with pink patch doesn't mean that the LLK pink nozzle contributes to QTR printing.
When I switch out of curiosity the 3880 printer from matte black to photo black, the nozzle test pattern shows two pink patches, the first upper left and as before the third upper left: Epson at work, not QTR.
So I'll leave things as they are, after switching back to matte black, and knowing that the LLK ink line is kept clean and open by the PFlush obviously still present in it.