I would recommend looking at the actual axis that it's using.
The camera forward vector is correct as I can draw a ray using the same vector and it points in the same direction with its origin at the camera position. The forward vector is the axis I am using but the resultant compound body motion is in the direction of what looks like a cross product result, i.e. at 90 degrees to the forward axis.
Are they the same in both the inverted and non-inverted case?
Only if I don't move the camera as it looks down the z axis (identity matrix, as you said).
Are the speed/dt values computed properly and non-zero?
Yes. I can use the same values for moving non physics engine objects around in the correct direction.