But for LCD projectors, a file's PPI is "scaled" to the projection size. In your example, does a "regular projection" size mean 1920x1080? Is that also the best viewing size (which I assume the jurors would use)? For this size, will PPI above 100 make any difference? When the projection size is larger than regular, what is the scaling formula? I assume that is PPI is "scaled" down significantly, it would mean a loss of quality.
You're making this a lot more difficult than you need to.
An LCD or DLP projector doesn't really
have PPI, except on the chip, and that's hardly useful.
If I project to a screen that's 1m wide, I get one density, and to a 5m screen, another one.
The only thing that remains constant, is the amount of image pixels the projector is capable of displaying.
If you deliver a file with minimum dimensions of 1920x1080, you'll probably be on the safe side for this kind of viewing. Most projectors do either 1280x768, 1024x768 or similar.
Semiprofessional or professional projectors, for instance for digital theatres, may deliver 1920x1080 natively ("2K resolution"), some even approximately 4000x2000 ("4K resolution"). The risk of anyone in a jury actually having access to a 4K projector is fairly low, the price is prohibitive even for theatres, but it's coming down.