Thanks for the reply and the link Logan.
The loopback test was one of the first things I tried. Not too surprisingly, it worked (or appeared to) just fine.
Through sheer desperation I managed to find a "solution". I posted what my findings were on the LAVA forums, and I'll quote that here:
The NI tech I've been working with also suggested using PortMon as a tool to help find the culprit. While I can't say for sure it's done that, it has done something rather interesting.
If I reset my IAI controller and send my first serial command with PortMon running in Local Capture mode, the command goes through. Not only that; but once the first command is accepted and returns a reply, all other communication works as expected with or without PortMon running.
I can even reset the controller. Quit LabView. Pretty much anything except reboot. If I reboot, I must start PortMon and reset the controller before sending the first command.
Once communication is established, Hyperterminal works fine as well.
Another recent (and very happy) discovery is that a USB to Serial converter is working just fine without having to jump through any hoops. As long as this solution continues to work, it's how we'll be going. But it still leaves me wondering why the included COM port was acting so weird. Obviously there's something going on here that may have effected other developers in the past.
Because this serial communication is only a small part in a much bigger program with the delivery date looming, I'm going to push ahead and really hope that the USB to Serial converter will continue to work for me.
This is one of those situations where neither company (NI and IAI) supports each others product. So I'm going to have to take what I can get and cross my fingers on this one.