I host a 70cm echolink node and did not need to place that PC in the DMZ.
I did need to forward UDP ports 5198 and 5199 to the PC running echolink. I don't remember whether I also forwarded TCP port 5200 or whether that "looked after itself".
You are right, only forwarding 5198 and 5199 UDP is sufficient. The echolink program also makes outgoing connects to port 5200 on the central server but you normally don't need to open or forward anything for that, it is just the normal outgoing NAT.
(there are instructions that mistakenly mention port 5200 to be opened, but the program is not even listening on that)
Rob