Who said you can only bring up enough for identification ?
You can bring up everything you find as long as you declare it in the country that you land it, and that is only if they have a law that requires you to do so.
If you take it to a country with no salvage or wreck law you can have the lot away.
OME did not commit a crime by recovering all the silver from the Mercedes, what they did was legal under International law and they voluntary declared it to a reputable court to establish ownership. As we know Spain was declared the probable owner, although the case was actually about Spain saying that the US court did not have the juristiction or legislation to hear the ownership case.
If they landed the coins in the UK, and ownership was declared to be Spain, they would have at least got a salvage award out of it.
The Victory is actually no different to the many wrecked HMS vessels that have been wrecked around the world that have been salvaged. It is only because OME is a responsible and reputable company that they contacted the owner on wreck location, they could have legally brought up all the guns without saying a word.
The laws only apply when you bring the stuff into a territorial jurisdiction.
Restriction on any recovery can only be made if a specific protection order is made to a particular wreck such as under the Protection of Wrecks act or War Graves legislation etc.
Look what they are trying to do to try and protect the Titanic, that shows you what lack of law applies to wreck in International waters and even now the Titanic only has UNESCO UCH protection, that as we all know is pretty worthless if someone really wants to work it:
The 41 signatory states, which do not include the U.S. and Canada, "will prohibit the pillaging, sale and dispersion of the wreck and its artifacts."
"They shall take all measures in their power to protect the site, and to ensure that proper respect is given to the human remains still to be found on it," the UNESCO said.
The Dutch salvors who raised a gun from the Victory knowing it was a RN vessel broke no law, and I believe the UK is yet to get the gun back, and I think they may still have to pay the salvor for some of their cost.
Legally the Victory site has no protection from any salvors and even OME could if the wanted to still go and salvage what they want, as the UK has no jurisdiction on the site and can only seek ownership in the courts of any country it was landed in (as Spain had to do in the US to seek ownership of the Mercedes Silver)