Can both jaws be rotated upwards? (Very important for professional maxillofacial surgeons)

Thank you for the great question. 
You have the essence of what needs to be done to achieve facial harmony.
To achieve this goal it would be ideal to treatment plan your surgery with a thorough facial and dental examination which includes cone beam CT (bone imaging) imaging and 3D facial photography (at rest and in smile).
In General, we want the facial thirds to be close to equal. If you type in "facial thirds" into any search engine, you will see what I am referring to. Thus, a counter-clockwise rotation as you discussed would be would be ideal, however the amount you showed  (and direction) may shorten your lower facial third too much (but its hard to tell without seeing photos of your entire face).
To achieve this rotation, you will almost certainly need a double jaw (upper and lower jaw) surgery. Double jaw surgery allows one to achieve complete control of lower facial third and achieve the ideal facial balance and harmony.
An experienced maxillofacial surgeon familiar with counter-clockwise movements and well versed in virtual surgical planning should be able to give you the result you are looking to achieve.