This is slightly related to the video problem people keep bringing up here. I can run this just fine in fullscreen and the videos work, too, but the problem is, my monitor switches resolutions when a video comes up, and when that happens, the screen goes black for a few seconds. Which means I miss out on the first seconds of the video.

Anyone have any suggestions?

First try Running the game in your native monitor resolution.

second try running the game in 640x480 Eww I know but it should help

I think you monitor is Auto Image adjusting if there is an option to turn it off DO SO.