I will again repeat my actual experience with doing this, that a simple pinhole box camera, positioned on a tripod in front of the screen at the approriate distance as per the formula I posted previously, is the simplest, most effective way to do this.

A glass lens capable of imaging the screen with little or no geometric distortion, and able to cover a large format, will be expensive and problematic.

Regarding the use of color film, you have, with a video image, the ability to alter its hue (i.e. color balance), instead of using filters over the lens/pinhole, so as to compensate for reciprocity failure of the color film that would otherwise throw off the colors in the resulting film image.