A possible second-best solution for orphaned antiquities?

This article in the New York Times describes how one art collector donated a work to the Prado, noting that 

he will be eligible for a tax deduction because the donation was made not to a foreign museum but to the American Friends of the Prado Museum, a United States-based charity.

The article also flags the difficulty of finding a museum willing to take "orphaned" antiquities:

Antiquities are particularly fraught, given patrimony laws that protect artifacts.

“You may have some great Egyptian artifacts and you’d love to have them in the museum when you die, because who else is going to take them?” Mr. Schindler said. “But if you don’t have good proof that they came out of the ground before 1970, good luck.”

This raises an interesting question about such artifacts. If collectors want them to go into a museum, should they be encouraged and permitted by countries of origin to donate their antiquities to a US nonprofit representing that country's national museum?

The downside, of course, is that donors will get a tax break for giving artifacts that might possibly have been looted. The upside is that the artifacts at least go back to the country of origin rather than back into the marketplace, and at far less cost in time and effort than would be necessary for restitution cases to be brought. In effect the American taxpayer would be underwriting the cost of returning artifacts to their original country -- though, it must be noted, never to their original find spot.