The first attempt I made, I tried my hardest to loosen it up, but as you can see, that didn't work at all. It is still as rigid and neat as a cross-stitch needs to be, is supposed to be. In order for me to, at least try to, lose that cross-stitch-neatness I decided to embroider on regular cloth. But it was not only the change in material that got me to this second stage; I also had to change my state of mind and try to forget everything I had ever learnt about embroidery. It resulted in a piece that is as far away as I could get from cross-stitch without it turning into something I was just sewing.
From these two extremes I began on my third attempt, which seems to be a good compromise between both: I drew the letters on my computer screen, traced them on the embroidery cloth and started embroidering without worrying too much about what is right and what is wrong. The combination of the loosely drawn letters and the cross-stitch rules, resulted in a playful, but undeniably embroidered logo. The best of both worlds I guess.
P.S. The logo is still being worked on.