Sorry, but you are misreading what is stated and the intent.
One of the statute's most important provisions specifies that the laws of salvage and finds do not apply to abandoned shipwrecks claimed by the government under the Act. This provision removes those shipwrecks from the jurisdiction of Federal Admiralty Court. It means that the shipwrecks and their cargo and contents are no longer treated only as commodities lost at sea and in need of salvage. This means that an historically valuable shipwreck can be treated as an archaeological or historical site instead of a commercial property.
It does not mean that the shipwrecks are fair game. It means that the Laws of Salvage and the Laws are Finds are not applicable. The cargo is not lost at sea, and the wrecks are not in need of salvage.
Admiralty Arrests cannot be filed on these wrecks.
Looking at the recent cases with the Spanish, Brits, France, and Germany, it seems all the US has to to is ask to foreign entity, and they all say yes. As noted, Germany has recently laid claim to all of the 3rd Reich property.
Looking at the research, I think it was proven that the Juno and LaGalga were sovereign, not abandoned, and the property of Spain. I do not see where it was proven that those sites were the Juno and La Galga.