I listened to the wise and did not try to piece the inner circles (they are just a bit too small for that) but tried raw edge applique (I think ;).
But, as I was eager to try Lynne's method, I used it for my first outer circle (you can see it on the left). I'm not sure this is how it is supposed to be done, but it works ;)
And I managed to finish the back of my pure hexagon park quilt, here's the pieced bit:
Now I'm waiting for the batting - it's the first time I'll be using cotton batting (I've been lucky - one shop here in Poland has decided to try it out.)