I DO NOT have GT4. But, it is my understanding that all of the menus in GT4 are in 480i in 1080i mode. So, when you actually strt the race, the video resolution changes. Alot of TV's and Projectors do some funky things when the tuner must realocate a signal for a higher or lower resolution. Usually only lasts for a couple seconeds, and then its disappears.
I imagine, this is whats happening here.
Also, your projector, does not natively handle 1080i. It may SUPPORT 1080i, but all 1080i signals must be downgraded. As 1080i image size is 1920x1080, its obvious there will need to be some image converting to get it to dislay on your 1280x768 display. So there is a likely hood that part of what you are seeing as well, is the video scaler catching up to properly scale the 1080i fed signal to display it properly, along with the resolution switch. And that causes the blind effect.
Keep in mind, i dont have GT4, and i dont have your projector, nor have i worked with one.
Im mearly throwing out some ideas bassed on what i know to be true with projectors, and HD displays from my own HT experience.