Let's say someone discovered a collection of dusty papers in the attic of a tavern that Ludwig van Beethoven stayed at in the late 1820s. It is a complete manuscript of the supposedly unfinished Tenth Symphony (the uncovered sketches were actually for his 11th). The discoverer sent flakes of the paper to antiquarians (who verify that it has the proper age), and photocopies of certain sections to renowned musicologists who can confirm beyond a reasonable doubt that the music is authentically Beethoven's.
The manuscript, otherwise unread by humans, is auctioned off and a big music company based in the US, MyTunes, purchases it for 8 million dollars. From that moment on their goal is to make as much money off this symphony as possible. They do not just want to own the manuscript, they want to own the 10th Symphony.
The tactic I envision for them is to restrict access to the manuscript itself (by storing it in a vault and encrypting every scan file so that it can only be opened when you're logged into the company's network), and have every recording made in their own private studio, with musicians signing NDA's. The resultant recordings would be theirs, and they would strike down any unauthorised use whatsoever. Music enthusiasts cry, but MyTunes sees their profits rise as everyone wants to know what Beethoven's 10th sounds like. If it is such a banger as the 5th and 9th, then every movie and commercial producer will want to use the music too. And later, they authorise their NDA orchestra to go on tours and give performances across the world, with heavy restrictions on the sheet music. Maybe they just have the orchestra memorise it everything, so no piece of paper carrying the notes ever leaves MyTunes HQ.
Now, leaks are of course going to be rampant, but I want to know if MyTunes' plan can be foiled legally. The 10th symphony itself is most likely going to be in the public domain everywhere, based on how long Beethoven has been dead, but by keeping the sheet music hidden, can that public domain material still escape their grasp?
What I am considering is people transcribing the legally obtained recordings, to get some version of the sheet music back. It's going to be difficult for some sections, but with millions of people cooperating, some version of the 10th is going to be restored. Is this transcription going to be in the public domain too? Can every orchestra and advertisement company make bucks off this open-source sheet music instead of paying MyTunes; or would it, as a transcription of copyrighted recordings of a public domain work, be copyrighted?
One way around it would be for MyTunes to drastically alter the 10th and never even record the original (or destroy it) therefore creating a new unique piece of music that they own, but a Quasi-10th Symphony is not going to be nearly as profitable as the real deal so they won't do that.
I have now put the legally transcribing part of the question on law.SE. Feel free to answer in the more general scenario, or with frame challenges to how MyTunes should operate to maximise the profitability of owning the only copy of Beethoven's 10th in existence.