You are correct, but also because we're hoping that this will nudge Rehnquist, which would simpify the entire nominating process.
Begin with elevating Scalia to chief justice, and backfill from there.
I wouldn't be surprised to see Rehnquist wait until O'Connor's slot has been filled to make certain that Bush can get an originalist on the court. But I have no evidence to support that claim.
I doubt the President would elevate a current Justice when Rehnquist retires. Why on earth would he want one more confirmation battle than he needs? For that matter, why would either Scalia or Thomas put themselves through that? Other than assigning the writing of opinions, presiding over the impeachment of a President, and prestige, the Chief Justice slot means no more than any other Justice.