K6 is K7 without shade 7 and the chart you printed tells us the inks are not in the correct positions, or have not been shaken prior to using, or have been contaminated accidentally, or the same ink is in two locations. So you are confirmed to have an incorrect installation.
The easiest way to determine shade placement is to read the installation manual for your printer model here: http://www.piezography.com/PiezoPress/technical-support/ This will reference each shade to each color position. This will match your ink shades up to the Piezography K6 curves. Without this perfect match the system will not be usable. So it is critical to follow the instructions for installation of the shades. That same installation of shades is available when reading the instructions for filling the carts. It is in several locations.
Moving the carts around is difficult in that prying off chips and gluing them back,etc may damage the pin readers, etc... It is not recommended. It would be better to start over with fresh carts and do it correctly. Trying to rinse the carts with distilled water may still not remove darker ink from some of the parts of the carts. Using anything other than distilled might introduce chemicals and matter into the inks as well as print head. Definitely not recommended.
BUT you must read our manual for using our system and it is also available at the above link. It is called the NEW Piezography Manual. We are not compatible with the QTR workflow in the QuadTone RIP manual. Do not follow their instructions when using our system.
So a lot to read before you get started...