First option:
Turn up the heat on the countries that aid and abet such evasion, such that they end up quitting the practice voluntarily. Offer to exchange information on theirs to gain wider cooperation.
Second option:
If cooperation cannot be attained, then take governmental action within the IRS to penalize such activity (as far as they can go). That doesn't mean taking a page out of Nixon or Obama, but to use any legal and Constitutionally approved means to stop the evasion.
Third option:
Start playing hardball through other legal means in other governmental entities. Their tax structure and obstinacy is enough justification. Offer large tax cuts that have a condition of taking a visible penalty or reward for tax structures.
Final (if nothing else at all works and something must be done) option:
The DoD does something outside of the US and K Street won't know the full implications until the public has a need to know.