I found an answer to my question, just including here for future reference.
I was referred to this Dtrace script [url http://blogs.corenetworks.es/2009/08/conntrack-dtrace-script-connections-by-process-user-and-port-on-solaris-opensolaris/]conntrack and it lead me to what processes were trying to use port 16001.
That lead to a couple of workarounds.
Installing [url http://www.liquid-reality.de/display/liquid/ESound+for+Windows]esound on the Windows machine and
in .bashrc on the Solaris machine. A user reported that he could set the value of the ESPEAKER environment variable to the Solaris machine itself and didn't need to use esound on Windows, but I did not verify this.
This problem with slow log out from Solaris Java Desktop using XWin 32 has been bugging me for months!
I've searched Oracle Support so many times and found nothing, but this has fixed it.
I figured looping it back on itself would be fastest if it works, and it does! I've added the following line to the .profile of my users who require XWin.
Log out now works instantly.