Songbird Puzzle Sonnet

The songbird sonnets flutter, dip, and climb
And trills his tune in manicky iambic
The song a blank verse jug-a-jug-a-jug
The nest he builds is borrowed, stolen stuff
Tra-la. Tra-la. Hey-ho. Tra-la. Tra-la.
As brave wren builds, the catbird calls, form free
With meters sweet, but rhymes anathema
He serenades from apple, rose, or lilac
The wren sings out iamb-iamb-iamb
Rebuild it line by line as twig by twig
Reweave this catbird sonnet now. The clue:
His nest a formless stick and twig discord
An endless glad-song, only slightly mad
If not an English rhyme, a scheme thereof