Don’t blame it all on the camera, although some does exist there (probably 1-2 frames). In all likelyhood the culprit is the projector itself, anywhere from 2 to 8 frames depending on model and resolution you are sending it. Also, you probably had a switcher in line which can introduce anywhere from 1-6 frames of delay.
To minimize the delay, send the projector a video signal at it’s native resolution. If it is not an HD projector that is probably 1024×768. Projectors are notoriously sloooow at conversion.
If you have a switcher make certain you genlock the cameras if you can. That will save a bunch depending of the model of the switcher.
Delays are additive to every component in the chain. You will have some no matter what you do. At 4-5 frames delay it will take a good eye to see it. 6 frames and anyone can see it if it is pointed out. 7 or more and the audience is annoyed by it. We make every effort to place imag screens to the side of the stage so that it is not quite as noticeable. The kiss of death is an imag screen directly behind the speaker.
Just some thoughts.
Jim