You and I have a very similar attitudes towards our turkeys (equally enabling!) You moved the garden to suit the whims of the birds... Yeah, I have done this kind of thing. Heaven forbid the bird not have everything it likes, just how it likes it! :jumpy
Are the cages in the run, or do the girls access this in your garden?
For vegetables I only use raised beds in an area the hens can't go. They killed all the flowers in the beds they could access (if the feet can dig up the roots, they do)
I wondered about making a tube out of chicken wire...
(Note: I am in the northern hemisphere, so the primary sun comes from the south in my garden, shade is created on the north side of objects during the hottest hours of the day)
I have a lot of small fruit shrubs (blueberry, gooseberry, Saskatoonberry etc) they are planted along the north side...