Your description of his stance with Hillary and health care is misleading. He led the Contract with America election in 94 which was a repudiation of Hillary Care.
That they agreed on some points later on is a bit unnerving, but your explanation is not accurate.
Gingrich has been very committed to the individual mandate in health care reform. That was one of the things (along with calling Paul Ryan's plan "right-wing social engineering") that put his candidacy in the toilet early on in the first place.
Newt Gingrich Had Lucrative Health Industry Ties , (one of many articles on this subject):
[snip]
The Center for Health Transformation, which Gingrich founded, raked in millions of dollars from heavy hitters like GE Healthcare and Wellpoint, as first reported by the Washington Post. The group says it does not lobby, but on its website, it touts its ability to build bridges between the federal government and private sector. Among its strengths, the think tank lists its unparalleled “network of allies” in the federal government, states, corporations and hospitals; “coalition building capabilities,” and “media visibility.”
[snip] He has blasted the individual mandate in the Affordable Care Act, saying in a video that he is “completely opposed to the Obamacare mandate on individuals,” and that he “fought it for two and half years at the Center for Health Transformation.” But the group, which Gingrich founded, actually supported imposing a mandate on those who made more than $50,000 per year.
CHT spokeswoman Susan Meyers said the group advocates such a move at the state level, not solutions that are “forced at the federal level” and that Gingrich supports “free market solutions.”
“We believe that any idea that states want to originate, that’s fine,” Meyers told ABC News. “It should be their prerogative if they choose to do that.”
Still, Gingrich hasn’t made that clear. In fact, he criticized opponent Mitt Romney for implementing such a “bureaucratic” mandate in Massachusetts.