I started testing some jumps and slopes with 60 and later on 50, 45, etc using riva tuner and the nvidia panel, I think that you could be right because I don't have a definitive proof of improving. I saw this problem in pc gaming wiki (https://www.pcgamingwiki.com/wiki/Area_51_(2005)#High_frame_rate_breaks_jump_physics) and changed it to 50 fps with riva tuner and I though that my jumps had improved. I'm going to do more tests later, if you solve the problem or you need something else make a post.
Yes, the jump mechanic is related to the fps, if the game plays above 60 fps the jumping mechanic breaks, that's the reason why it's capped, the problem that you say is that it's hard to jump on slopes or small areas. For some reason when you play above 50 fps you loose "grip" and it's much harder to jump, try playing at 50 fps capping it with Nvidia panel or rivatuner. If it's useful if you play at 10 fps or below, you jump a little bit higher, very useful for the moon landing skip.
It would be awesome, i think the same about cutscenes, withouth them we could probably beat the game under an hour. I knew that you could remove the cinematics cutscene of the start of each level by removing all the files in the movies file (these are skipeable), but can you remove the in-game cinematics?
I found a new skip in "Lies of the Past - Chekpoint 4" where you can skip the whole moon landing part, if you lower the fps to 10 or 5 you can jump a little bit higher so this allows you to do a jump that skips this whole part.