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You could try this http://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exch... Although, it would depend on finding a pre-existing implementation (remember it is a bad idea to implement your own crypto). Is there are trust-worthy source of random characters available?

Well, Diffie-Hellman wouldn't work very well for this since any conversation between my server and the client would take a long time, unless I'm misunderstanding what you're suggesting.

The motivation behind the scheme I came up with is that it could be done with no pre-communication, hence why my RSA public key would be hardcoded into the client.

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