I like your order, but Cora's not going to demote Story; AC doesn't read forums, so he actually believes what he sees in Spring Training.
As for wherever Anthony bats, it's ideal as long as guys are getting on base in front of him. No matter how optimistic people are about the rest of the returning regulars, they're all career .250 hitters with big swing and miss.
Roman is the best hitter with the most consistent hard contact rates, so it's imperative this offense positions him to drive in as many runs as possible. I understand getting the best OBP guy the most ABs possible, but in this offense he'll be more valuable with the most RBI opportunities.