I wonder whether this is actually a problem. Compacts only have constitutional force if they are approved by Congress. Presuming Congress would pass such compacts into law, they should arguably have the equivalent force of law as the Health Care Choice Compacts clause of the PPACA. Their direct contradictions of the PPACA would arguably supersede the PPACA. Yes, the principles of statutory interpretation put a high premium on reconciling all federal statutes as much as possible, so a federal judge might shoehorn a contravening compact into the Health Care Choice Compacts clause and read it accordingly as subservient to the PPACA. But if the compacts were written in sufficiently strident and contradictory language, it would be an easier argument to say that Congress's later approval of these compacts would override the PPACA, as both would have been Congressional actions. Otherwise, the net result would be to say that Congress cannot abrogate or repeal its own laws—precisely because for compacts to pass constitutional muster under the Compacts Clause, Congress has to expressly write them into the public laws.
The compacts would not likely survive a legal challenge if the states didn't seek Congressional approval but just made bilateral or multilateral agreements outside the Compacts Clause of the Constitution. And because such compacts are not recognized as having the constitutional force of law, they would likely fall under the Secretary of Health and Human Services's purview, whom Congress has delegated through the Health Care Choice Compacts clause of the PPACA to give approval to conforming compacts without Congress's further involvement. Whether that is philosophically constitutional is another question, but my sense is that the courts would not hesitate to uphold the Secretary's authority under this provision.
Of course, there are also political rather than legal factors at work. If a sufficient number of states made Tenth Amendment assertions opposing the PPACA or agreed multilaterally not to assist enforcing it, the federal law might become practically moribund with or without Congressional involvement. But I suspect that a "sufficient" number of states would be fairly high—38 maybe?
