If the random number scheme is subject to evesdropping, which it would be over todays net, then the numbers you use, while they may show no pattern, could be known to an attacker, which would probably make them far less useful. A better way to spend your time would be to design a bit of public domain hardware that could be easily built by anyone who wanted a hardware rng.
Not really, the receiver of these numbers could run it through several crypt programs with random keys gotten from his machine, etc. If you do several hundred rounds with several hundred random keys with random delays, the random numbers resulting from all this abuse should be quite different from anything that whoever is spying on the transmission will see... (Granted, though this would still be a PRNG, it would be better than most, if the purpose of these random numbers is to simply act as a RN server.)
If you include the signatures of the previous several messages in the signed message, and issue each a message ID, changing the time becomes easier to detect. If you keep all messages signed that week, and publish a checksum in an easily found source, say the New York Times, then you're repeating work already done at Bell Labs. (I'm sure someone could find a reference if anyone wants to get in touch with these folks?)
I haven't heard about this... can you tell us more?