Gary Bauer is a good example. He is to the left of Bill Clinton economically, but a devout moralist christian, so he is called a conservative. Is he?
I think the words get confused. Conservatism means just as it says, to conserve, to preserve the moral order. But in a time when the order is chaos, the meaning of conservative is thrown into the abyss as well.
I would argue that Gingrich is more of a reactionary than a conservative. Reagan was trying to reinstill old values, so he was conservative, Gingrich was interested in new ideas, etc...
Is Free trade or protectionism conservative? Are the steel tarriff's Bush adopted conservative? Is the federal war on drugs conservative? It all depends on your definition.
I think your examples are either conservative or populist positions depending on the stance taken.
By that definition, I should think Gary Bauer would fit right in. He is about the most moral politician we have, isn't he?
Or by moral order do you mean "social order?"