Suppose HCR gets overturned in the Supreme Court? Then what?

This is currently allowed. In fact, most large health insurance companies do exactly that.

The GOP proposal, as I understand it, is to allow me, living in Missouri, to buy a policy from a company that is only licensed in, say, Arkansas. Said policy would only meet the regulatory guidelines of Arkansas, not Missouri.

Any reduction in costs this would generate would come from either (a) insurance companies flocking to the least-regulated states and offering these minimal policies nation-wide, (b) increased competition driving down premiums nation-wide, or (c) better risk-pooling by allowing insurers to have access to a broader market rather than just the state or handful of states their licensed in. Obviously different experts have different opinions on which of these would predominate and how large the savings (if any) might be.

Finally, the PPACA included something similar to this, allowing states to enter compacts that allow for insurance policies across their borders. Additionally, multi-state insurers will be allowed in underserved markets as long as they meet federal minimum coverage guidelines.

What way would that be?

As far as I can tell the only health care reform promoted by Republicans in the last couple of decades was the one that was passed in 2009 and signed by President Obama. First it was promoted by Newt Gingrich in response to “Hilarycare”, then a lot of it’s properties were touted by some conservative think tanks during the Bush administration, then John McCain supported mandates during the 2008 campaign, and Romney supported something very similar to it in Massachusetts. So now that it has been signed into law by our Demcratic president, what are the Republicans wanting to replace it with?