Well, the English version provided are now ambiguous in new ways, I think. The goal of the original was a group both musical and English, the "incorrect" was a group doing English music. We now have a group from musical England, too.
As far as I can tell, all these examples (and the judgments on them) are Lope's, not taken over from Pije or Sonja (who, so far as I can tell, don't object to nested 'pi's on grammatical grounds, though likely on aesthetic and semantic ones).
'la' differs because being a condition for something else inevitably sets up a hierarchy: you can't swap around the "if" and the "then" part with sentences, for example.