Kinematic model for a 5axis mill with universal (nutating) head

Please repost your question.

The kinematics in this thread is for head-head rotation. Your machine is a table-table rotation type.
I suggest looking at the simulation configurations found in the 'configs/sim/axis/vismach/5axis/table-rotary-tilting/' folder. Most likely the 'xyzbc-trt' configuration will fit your machine.

The Tilted Work Plane feature I implemented is for kinematics with tool side rotation only. For machines with work side rotation, like yours, prismatic machining is much easier since the XYZ linear axes are always aligned with the tool, so all you need is trivial kinematics to orient the work and do the machining.
So implementing Tilted Work Plane for work side rotation would actually be easier but it is unfortunately not covered by what I did.

Not sure which paper you are referring to but I have this matrix for rotation around Z:
 

which seems to correspond to your version.