Compressing the videos using H.265 instead of H.264 would reduce the size greatly, without having to renounce to videos.
Removing the audio stream would help to reduce the file sizes too.
I tested this theory with one of the biggest videos in the game, named 12.mp4, without saying a thing about the convenience of a 10 minute video in a QSP game...
The original file is 143 Mb.
I used Handbrake to recompress the video, h.265 quality "32", max 24 fps (instead of 30), and no audio stream.
The new video created by Handbrake (5 minutes of processing) is a 18,3 Mb. MP4 (M4V) file.
I won't say is the same quality of the original video, cause there is some compression, but there is very little difference.