OK, here's how it's done! It took me the rest of today to figure this out. The gentleman from Spectracal was right. Joel (from Spectracal) was correct that JRiver (and other video playback programs) normally ignore the profile and yes they do. But there is
a way to use icc monitor profiles with a video playback program and just the i1 Display Pro! I figured out how to do it with just the i1Display software and some utilities available free from XRite; so I wouldn't have to buy another calibrator from Spectracal (sorry guys). I think this post should be made a sticky.
Damn Windows, this would be so much easier on a Mac. When I started this investigation I thought I had licked the problem, but on a reboot the monitor calibration was lost. So I had to do a little research and come up with the recipe below.
The way to do it (as mentioned by Joel from Spectracal) is to load the gamma curves into the Look Up Table (LUT) of the graphics card each time you start up. I have an AMD graphics card, which does not allow loading icc profiles directly. The following procedure may not be necessary with NVIDIA graphics cards as apparently they have a method of initializing with an icc profile.
1) The monitor profile must be applied to the look up table (LUT) of the graphics card each time that windows is restarted. Since JRiver won't use windows' icc profile, then the profile (or its curves) must be loaded directly into the graphics card!
2) The LUT (lookup table) in the graphics card must be reinitialized with the icc profile (gamma curves) each time that windows is restarted, or the monitor profile will not be used by your video playback software.
3) Download from the i1 site "Eye One Match Software". Most of this software is not appropriate for the i1 Display Pro and will not function. However, XRite includes one gem which is essential (and apparently does not come with the regular i1 Display Pro software). This is a LUT loader called "CalibrationLoader.exe". Put a shortcut of this application in the windows startup folder.
4) Also download from the i1 site the "Calibration tester", known as pm5_calibration tester. You can use this to confirm that your graphics card has loaded your monitor profile, and also to disable it to see a before and after demonstration. You can then reload the monitor profile using "Calibration Loader" to test it. Both of these files are found at http://www.xrite.com/product_overview.aspx?Action=support&ID=758
at the xrite site.
5) Make sure that your i1-generated monitor profile is the default system profile in the color management section of windows. This is the profile that will be loaded by "CalibrationLoader".
6) If you are using Photoshop or other application which can use a monitor profile on this same machine, be careful that you don't get "double correction". You may have to clear the LUT override on the graphics card in some circumstances. And if you are switching back and forth frequently between Photoshop and JRiver (or similar video playback software) you might be able to set up an autohotkey macro to perform the switching tasks.
Attached are two screenshots from "Calibration Tester" on my machine. One of the shots is after loading a fake "crappy profile" that I generated using the Sony monitor set for "vivid" to fool i1. It's great for testing and proving that your correct monitor profile has been loaded after restart. The other screenshot is the results of the i1Profiler, it is my icc profile that I'm now using to get beautiful-looking and accurate video from JRiver. When the LUT is cleared with the reset button in Calibration tester, the graphics card is neutralized, I cannot see the 2% chip in the pluge pattern, and the grayscale looks uneven and color-tinted in spots. When I load the "crappy profile" everything looks crappy so you can really see the effect. Finally, when I load the correct profile, all the chips are neutral gray and the pluge pattern looks correct. This holds through reboots! Hooray.
I can only conclude that I've conquered the problem and that the i1Display Pro can be used with video playback software.