It took a couple tries and a little troubleshooting, but I have it working.
I needed to do 2 things to make it work, over and above allowing traffic through port 65000 (the port I have selected in Limewire).
1. I opened port 6346 TCP & UPD for inbound & outbound traffic.
- This is the port required for the 'port test' from #10 on the "provide your system details" page on this site, but I didn't see that it was documented as being required to be open for use with Limewire
2. I ran Limewire with ALL ports open on my firewall (i.e. similar to Bob's suggestion of going through the DMZ)
until Limewire connected for the very first time- Once Limewire connected successfully the first time like this, I then restricted my connection back to only port 65000 and 6346, and Limewire still connects successfully.
I've repeated this same process now on 3 different PC's on the network, and each one of them did require both steps #1 & #2 for Limewire to work. If I skip step #2, Limewire doesn't seem to want to connect the first time, regardless of reboots, reinstalls, deleting folders, etc., almost as if it needs to initialize on some other port the first time. Coincidence? Requirement? Not sure...
One other thing I noticed...
While I had ALL ports on my firewall opened, Limewire connected with a "Full Connection", but as soon as I restricted it to ports 65000 and port 6346, I now only get a "Medium Connection". Does this mean there are other ports that I should have open to get a better connection? Is there a resource that will tell me *every* port that needs to be open for Limewire?