Can you not see, from your own posting, that there are four pairs of ports, and each pair has to communicate in both directions?
I've listed the 8 data streams I've seen described by the OP. They use ports 8020, 8019, 8008, 8003 to send from, and ports 53036, 53037, 53038, 53039 to listen to. I haven't seen the OP describe traffic originating from ports 53036, 53037, 53038, 53039.
But whether or not there's bidirectional UPD traffic, that's irrelevant. I still don't see 2 processes trying to use the same port. Can you point out a port, and the two processes that need to access it?
It is implied by the OPs description.
The pre-existing server might be,
Most services restrict UDP packets to be at most 512 bytes. But even if they don't, UDP packets are restricted to be at most 65535 bytes (as the length field of the header is 2 bytes large), leaving slightly less for the payload. I just haven't assumed the OP runs hardware that needs more than 10 seconds to copy 65535 bytes from the IP stack to the process' memory.