Well, its a simple fact that, if you are running it through Wine on top
of a shaky internet connection, its very difficult to figure out.

I for one am not totally sure it is the ports to begin with. There are
so many other issues that could be the problem.

On the Ubuntu list one of the responses to your post was that nat
probably has to be working for the return response.

It may simply come down to this:

Internet connection -> Linksys Router -> pc1, pc2, pc3

You might just have to purchase a router (with or without wireless
capability) for this to work.

George said that he got the app working just fine on his set up so I
have a strong suspicion that this isn't an Ubuntu problem but a network
setup problem.

I would suggest this: simply your setup.

Get the modem on your Ubuntu computer.
Start echolink and see what happens.
Did it connect?