I am in need of being able to tilt / rotate the player while they are seated in a chair. Is there any way to set the angle of the player when they are using a piece of furniture? I have tried SetAngle on both the furniture marker and the player himself. In the first instance, the chair moves while the player remains fixed. In the second case, it causes the player to dismount the furniture. Also, I have tried SplineTranslateTo, and specified the destination angles for the furniture object, with no success.

Is this possible?

This is extreme, but is it possible that instead of rotating the player+furniture, you rotate the room they are in instead?

*EDIT: I've noticed that if you remove the IsJarlChair keyword (or whatever it is) and the Forced3rdPerson keyword from furniture pieces that have them by default you get some quirky behaviour. You seem to be able to rotate within the chair. This is ugly though are you will see parts of the player's body (floating arms) incorrectly.

Since this occurs in the Tamriel worldspace, no, I can't rotate the world

Haha, I had a feeling you would say something like this.

*EDIT:
Just in case you didn't see. You posted just before I edited that post.

Thanks Antares.

I don't mean just on the z axis (left-right), I also mean front-back, x and y axis rotation. Imagine the player sitting in a chair, upside down. Something like that.

Sitting upside-down would certainly be novel. Vertical sleeping NPC's would be pretty cool too (vampire style).
I thought you'd appreciate knowing that it is somewhat possible.

This has expanded to needing to be able to show the player laying down at an arbitrary (script-defined) angle. Is this possible?

Currently, when my character is using a bedroll on a steeply graded slope, his head is stuck in the ground and his legs are out in the air. I'd like to be able to rotate the marker, or the player, such that they display correctly. Is this known to be possible via any means? I'm willing to be creative about the solution.

There must be some property or other which dictates orientation. From your post it sounds like being parallel to sea level is somewhat hard coded, perhaps if you were to rotate the mesh in nifskope so that the native orientation is offset? (ie when you drop the object into the editor window it automatically appears at the desired rotation)