Enter the 1099-Misc exactly as received. Do not change it. TurboTax (TT) will do that for you. After identifying the reason for the 1099-Misc as "prize", you will reach a screen called. "Fair market value of prizes and awards". There you will enter an adjustment for the prize value. In your case enter -17,100. TT will enter the 1099-Misc amount and the adjustment on line 21 of form 1040 (Schedule 1).
As an aside, I believe your suggested adjustment is over stated. Just because the room was complimentary to the game show, doesn't mean it had no value for you. The fair market value is the going rate for the room.
