I can't comment on the mathematics involved but let us assume it's mathematically possible. You engineer this mythical nearly foolproof backdoor. You can decrypt this text with any of two keys. (It's my understanding that such algorithms actually exist already.) Congratulations you have achieved your goal. You have a working algorithm.

Now let's examine the results of actually using this algorithm:

You now have twice the opsec problem you had before. You have transmit this second key to a Government agency securely. You have to trust that Government agency to securely store, use, and dispose? of this key when they obtain it.

And what is the number one threat to secure systems? Operational Security. In fact many security professionals will tell you that the hardest part of security isn't the math behind the encryption. It's the opsec. In one fell swoop you double the threat in the most fragile part of your security.

To make a car analogy, we can make a submarines that are waterproof, and we can make cars which looks like a car and you can drive on the road. However, to make a car that is also a submarine is quite hard, and close to impossible if you also had to make it look like a normal car. It would even be harder if it need perfect obscurity so that you couldn't even tell if you opened up the hood or started to disassemble the car.