Like Earl Warren, or Anthony Kennedy, or Harry Blackmun, or Warren Burger?
Souter's record said he was conservative. So did Kennedy's. So did O'Connor's.
Judicial record means nothing when they get up to that court.
For example, everyone is saying "Maureen Mahoney" should be the replacement. Mahoney's bio shows that she was the lawyer of record who won the Michigan State Affirmative Action case for the democrats. When asked if she didn't have a problem with that because of her supposed conservatism, she said that she had "no problem" with the result.
Put this widely acclaimed "conservative" on the court, and you're no closer to your goal than if you had Miers there.