I think you're correct. I can handle the incoming packets on the same thread. This was actually very helpful because I forget that UDP is stateless - hopefully my bone-headed question helps someone out in the future.

My goal is to create a simple SIP proxy in our very non-standard environment. So, what I should do is create a fork (or what-have-you) for each new unique conversation identifier (as required in SIP) and do exactly what you said in your third paragraph.