I dont know how experienced you are,but I would suggest you try to find a really experienced turner for a second opinion ,if they cannot get good results then I think that you should dump the lathe on warcos doorstep stating that the machine is not fit for purpose, the tailstock height difference is a fault that should reject a lathe, I googled the lathe type and it appears tp have a vee and flat bed,a saddle traversed on this type of bed should not cause any of the deflection described particularly when traversing by hand .
refering to the comment on chatter and ringing when turning thin tubular shapes, this will occurr on any lathe,its the nature of the bell like shape, the work needs some vibration damping applied, during my aprenticeship I was making some 3 inch dia micrometer drums in brass . I bored them out ok but when turning the od and the taper where the numbers go it really sang and vibrated ,foreman showed me what was apparrently an old trick,fill up the Inside Dia with a thick greasy rag and ram it tight with a screwdriver handle ,vibration ceased, Of course depending on the job ,internal chatter on a thin bore is more difficult to cure ,a damping material can be clamped on the outside dia, or a larger piece of material used,bore to size,vibration should not occurr with the thicker wall material ,then turn the od to size.