I'd keep Ortiz and Beckett. Ortiz has nasty stuff, and going to the Braves won't hurt. If anything, working with a new coaching staff might bring him closer to his full potential.
Beckett is a risk - a very large risk, in fact - but his ceiling is as high as any pitcher not named Randy currently playing in the majors. If you don't like taking risks with your keepers, drop him, but I think the possible reward justifies taking a chance.