Walter, I hope you haven't given up on getting a response to your question because it is possible I may have an answer. I needed to consult with someone first, thus the delay. I have experienced the same problem with clipped highlights (and shadows). Here is how it was resolved.
Please forgive me if you know any of this already …
Basically projectors are set-up out of the box to provide a bright contrasty image in daylight. But many (most ?) can be set to a variety of internal 'profiles' which, for the projection of photographic images, the better will be called something like “photographic” or perhaps “sRGB” (some experimentation will be necessary). This can set the projector to (hopefully) give a satisfactory image in terms of brightness, gamma and contrast. Another way of improving clipped highlights may be to run the projector in “eco” or low–power mode.
When you've decided on a satisfactory set of internal settings for the projector then you can then profile it. The resulting profile will ‘drive’ the output from your computer to the projector. But then, of course, you must ensure that the internal settings of the projector do not get changed or this would invalidate what the profile is trying to do.
I'm not familiar with how Windows manages all this but my guess is that the profile has to be selected in the Control Panel(?) for the projector driver. I managed to achieve this on a Mac.