What you are mentioning here is the problem of trust, which is the major and unsolved problem in IT security.
Despite maths and algorithms, everything in security is ruled by trust in the parties with whom you transact.
What you have illustrated here is a huge human factor problem that has economic and political implications.
One thing you forgot to mention, is that the Big Corporate might be issued a Government (secret?) order to keep the keys. So the whole thing has a lot of implications.
My theorems about Computer Science
The following applies to the current scope
Once a piece of information is copied, it is no longer under your control
Every piece of information stored in digital computers must be made a copy of when getting transmitted
Digital computer primitives are only
I could go ahead and expand #3 in Turing-equivalent machines and algorithm theory. Once a secret key is stored in terms of bytes in a Turing-equivalent machine or a mass-memory readable by a Turing-equivalent machine, it can be made infinite copies of
Technical Solution: a true DRM framework
I would think about opting for the following kind of solutions
1. Theoretically, use quantum computing
Those machines are not commercially available today on large scale. One of the key principles of quantum computing is that certain particles may share the same effects at distance (quantum teleporting). Scientific research is working on that.
You may think about storing secret keys in quantum particles, so that you can "destroy" them (destroy or alter the information stored in them) from your office, even without network connection, and without the counterparty to make a copy of the quantum keys.
2. Practically, Try to employ encryption hardware
You may design your crypto system to rely on hardware devices. Apart from advanced techniques of register-reading on hardware, which is extremely cost, you may find it useful to use a machine (e.g. programmable smart card) that destroys its keys after a certain amount of decryptions.
A time-based disposal requires additional hardening in order to authenticate the timestamp or prevent the smart device's clock from being altered.
Since encryption hardware prevents the keys from being copied, this is the only technical way to make sure your contractors obey. You may also demand them to return the device once they finished with it
3. Another approach is to use multi-escrow keys
You mentioned "without conspiring with too many people". One of the things I loved from certain Bitcoin wallets is the ability to designate a quorum (M over N) of cryptographic signers for a transaction. Let's revert Bitcoin's example here.
Given N a set of secret keys, and given M the minimum number of keys to fully decrypt the piece of information, you may design M and N to be enough large for the conspiracy to be excessively large (too many individuals to bribe/threat?) and M to be enough smaller than N so that if one of the people holding the keys may fail, even physically.
Example: 13 over 25 means that you create a set of 25 keys so that a minumum of any 13 is necessary. 14 is the minimum number of people to bribe, and that if 12 or more people fail you lost your encryption information forever.