Determining absolute configuration when the lowest priority group is not facing backwards
You had the right idea when you said &quot;if the hydrogen is coming out of the page (i.e. as a wedge) we swap our answer from R to S or vice versa (to get the hydrogen going into the page)&quot;.
The difficulty seems to have came with your manipulation of the drawing. The diagram you have implies that the hydrogen is coming out of the page towards us (i.e. anticlockwise = (R)).
You could also flip the entire molecule through by 180° to give you the chlorine pointing out of the page towards you.