Ok. After fiddling around more with the files, I got a bit further.
In pak024.pk4 and pak025.pk4, there is a much smaller version of the Activision logo video, which I assume is there to replace the original one that is now no longer used due to the game now being published by Bethesda. So I took that smaller file, copied and renamed it, and replaced all the other videos with it.
The videos are in
pak012.pk4
pak023.pk4
pak024.pk4
pak025.pk4
under the 'video' subfolder. You can open these with, I assume, any unzipping software. I used 7zip.
Running the game again, instead of the intros, I got a black screen... and the sound from the videos before the menu opened.
The intro videos, it turns out, are made up of separate video and sound files. The audio files are in
pak010.pk4
pak025.pk4
under the 'sound\cinematics\bumpers' subfolder.
So I went about replacing those with empty audio files. And that got me a lengthy black screen before the menu opened. I also created a new .pk4 file with all the empty files I'd created/copied in the hopes that I could come up with a fix that didn't require diving into all of the other ones, but that produced the same result. The black screen went away after I hit 'escape' three times, exactly like I was skipping the normal intros manually.
It would appear that the game is set to run the intros for their proper duration even if you remove the files. If there's a way to fix that, I don't know what it is, or where to start looking. I think this is going to be the end of my investigation.