I regularly transfer my slide programs to video quite successfully using a matte white screen and projecting directly from the projectors, which are positioned about 10 feet from the screen. I place the video camera alongside the projectors and adjust the zoom lens and tilt adjust the tripod to fill the screen with the picture. Slides have a 2:3 ratio and video is 3:4 ratio, so you crop a bit if you want full screen video. You can also back off on the zoom so the full slide, either horizontal or vertical, is covered. The angle of camera to screen causes a slight keystone, but not objectionable at all. Much easier than using a rear-projection method and, I believe, the picture quality is better too. Let the camera run on full auto and white-balance and exposure track pretty good. I usually get a little more technical and set the camera on manual exposure and set the white balance manually with just straight light from the slide projector.
Good luck. Ron