Hello Dno.   I'm not familiar with the show so I don't know how "seemless" or complete this scene change must be, but that has never stopped me from making suggestions before. 

Can you build double sided flats on wagons so you can spin your wagons to become the courtroom?  Could the "fireplace" turn to reveal the judge's bench? 

Another quick scene change involves "booked" flats.  Your courtroom flats are hinged to your livingroom and swing into place at the appointed time. If you have flyspace, I assume you've already considered flying your scenes in and out.

Your point about the black light and white clothing is well taken, but I should point out the light will also have an effect on the look of your actors teeth.

One last idea.  Scrim.  If you have a whiz at painting, scrim is a beautiful thing.  When lit from the front, the scrim painting is seen, when the drop is lit from behind, the scrim becomes transparent and we view through the fabric. 

Empty your mind and imagine.  You will come up with an elegant and workable solution.