I would consider buying a replacement collet nut, possibly from a different source, although this may be tricky, as they have omitted to specify the collet system they are using. As you suggest, they are supposed to extract the collet, since taper seats with such a narrow taper angle are not inherently self-releasing.

I take it you have oiled the chuck before tightening and the collets are clean and unblemished? Do you leave the cutter in place when trying to release the collet -- this might prevent the collet from contracting and give you just enough engagement with the nut to make a difference.

I notice the instructions don't address removal of the collet. Your problems may be simply the result of poor design and/or quality control (it's probably made in China anyway) - German and Swiss manufacturers love to trade on their supposedly superior engineering when reality often results in a different experience. Speaking as the owner of a 4 wheeled money pit.