Asymmetric encryption is very computationally expensive - there's a reason that it's typically only feasible to use for signing a hash or as part of a key exchange to agree upon a shared symmetric key.
Envelope encryption works for that - client generates a random symmetric key, encrypts the data symmetrically, then asymmetrically encrypts just the key (which is then thrown away on the client). Both the symmetrically encrypted body and asymmetrically encrypted key are sent.
You just modify the client to leak the data before it's encrypted symmetrically. Keys don't matter at that point.