We had a standard award in late May `06 and had no problems and booked two months ahead... the award capacity issue is definitely true for Rome... but Capri was a breeze for us...
definitely have dinner at L'Olivo (Capri Palace Hotel and Two Michelin Stars) and D'aPaulino in the Lemon Grove.. a NY Times article a few months back also had some fantastic reviews...
Capri is a fantastic place... i hope you make it there.