As long as they remain US citizens the tax laws apply. If they stop being US citizens make them register as foreign agents and publish all lobbying attempts. In addition we should make any organization that is not >50% owned by US citizens a foreign controlled entity and remove their ability to lobby in private. There are other changes that would need to happen like making it illegal not to be able to trace ownership of an organization to an individual but its better than nothing.
At this point almost anything is better than what were doing now. Its getting really old feeling like we're a hostage to these people. If they are to tied to the economy as a whole that doing something as simple as making them pay a fair amount of tax they need to have assets stripped from them until they aren't a theat any longer.