A letter from the Fish & Wildlife Service stating they can't sell it to a museum - even though it's already on display in one - is what would show this; but if they asked, they would not get that letter - they would be told they could, for the same reason that they could keep it. (Because this is a famous, exceptional, well-known piece that is attested as being produced before the law that made it illegal.) The conditions would be the same - it would have to go in a museum.
You have to realize that under the law you're quoting it's illegal to POSSESS as well. This is what changed my opinion of the case.
So the family is saying "it's illegal to own or sell", so we'll just do the former since we already got approval but we'll say we can't do the latter, and won't even try to get approval.
Personally, I think they should put the price that a museum would pay (and not a recluse billionaire) and which they would expect the Fish & Wildlife Service to approve. Or they can ask for that approval, which the article doesn't show them doing. If they asked and the Fish & Wildlife Service said, weirdly, "you can keep it - as long as it is on display in a museum - but you can't sell it to that museum" then the article, and you, would have a case.