Fascinating read, and I think they cover the actual reason for this occuring so much more on these now barren islands where it doesn't occur in anywhere near the same numbers in other places that the eagle has been reintroduced; the hills are barren from humans clearing them in the early 20th century, there is no tree cover and consequently significantly fewer alternative prey for these eagles, less shelter for lambs and sheep, and less biodiversity.
The reality of the situation sounds like the farmers and their livestock would benefit from attempting to reforest, atleast in part. It would take a good 15-30 years at a minimum before forest would be regrown enough to enable other prey species to thrive, but it is probably the best option for keeping the places viable as farms without eradicating the eagles.