This is something I worked on for about 5 consecutive hours. It is a combination of Nash's Tilt++, Zombie Killer's footsteps, and a new version of my RealAim script combined with Thief-style leaning. Your camera will tilt and bob in harmony with the sound of your footfalls, all synchronized to bring a heightened illusion of actual concerted bipedal movement.
You probably won't like this if you get motion sick easily or don't like any form of move bobbing or dynamic weapon inaccuracy.
Screenshots won't really do this mod/mutator justice, seeing as it is entirely about the camera in motion.
Download the latest official release (v1.0.4) here.
I intend to expose this thing's terrible guts on GitHub at some point in the future. It's mostly the listed mods stitched together and made to share a couple variables here and there. It's rough around the edges in its presentation, but it seems functional.
Do play around with the in-game options menu for Immerse, as it is unlikely to look good out-of-the-box. For instance, you would use very different settings for something like Hideous Destructor as opposed to Smooth Doom, since the player's movement speed will be considerably different between the two.
This mod contains scripts and code by Nash and The Zombie Killer, so a big thanks to them. I believe I've left comments in the .pk3 indicating who wrote what code, but if my credits aren't up to code just let me know and I will correct the situation.