I don't think Hillary is running as a moderate Republican anymore than John Kasich is running as a moderate Democrat.
From Five Thirty Eight (Nate Silver's website) Hillary Clinton Was Liberal, Hillary Clinton Is Liberal:
"To see how these different issues fit together to form an overall political ideology, we usually use three metrics: one based on congressional voting record, one based on public statements and one based on fundraising. Clinton was one of the most liberal members during her time in the Senate. According to an analysis of roll call votes by Voteview (http://voteview.com/), Clinton’s record was more liberal than 70 percent of Democrats in her final term in the Senate. She was more liberal than 85 percent of all members. Her 2008 rival in the Democratic presidential primary, Barack Obama, was nearby with a record more liberal than 82 percent of all members — he was not more liberal than Clinton. Hillary Clinton also has a history of very liberal public statements. Clinton rates as a “hard core liberal” per the OnTheIssues.org scale. She is as liberal as Elizabeth Warren and barely more moderate than Bernie Sanders. And while Obama is also a “hard core liberal,” Clinton again was rated as more liberal than Obama.... Overall, the “liberal Clinton” isn’t a new phenomenon. Given her support for liberal positions in the past and the support that liberals have given her, it shouldn’t be surprising that Clinton is staking out liberal positions to start the 2016 campaign."
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From Five Thirty Eight (Nate Silver's website)
Hillary Clinton Was Liberal, Hillary Clinton Is Liberal:
"To see how these different issues fit together to form an overall political ideology, we usually use three metrics: one based on congressional voting record, one based on public statements and one based on fundraising. Clinton was one of the most liberal members during her time in the Senate. According to an analysis of roll call votes by Voteview (http://voteview.com/), Clinton’s record was more liberal than 70 percent of Democrats in her final term in the Senate. She was more liberal than 85 percent of all members. Her 2008 rival in the Democratic presidential primary, Barack Obama, was nearby with a record more liberal than 82 percent of all members — he was not more liberal than Clinton. Hillary Clinton also has a history of very liberal public statements. Clinton rates as a “hard core liberal” per the OnTheIssues.org scale. She is as liberal as Elizabeth Warren and barely more moderate than Bernie Sanders. And while Obama is also a “hard core liberal,” Clinton again was rated as more liberal than Obama.... Overall, the “liberal Clinton” isn’t a new phenomenon. Given her support for liberal positions in the past and the support that liberals have given her, it shouldn’t be surprising that Clinton is staking out liberal positions to start the 2016 campaign."
Source: http://fivethirtyeight.com/datalab/hillary-clinton-was-liberal-hillary-clinton-is-liberal/