No need to adjust as what the government pays today include taxes of the suppliers and all upsteam producers. Since the entire income and payroll tax system is replaced by the FairTax system, the gross (tax plus price) paid by govenment remains constant with what is paid today.So, you are assuming everyone will take a pay cut to facilitate this price drop? Your assumption that producer prices will drop has been blown out of the water.
Actually it looks like the economists figure for a takehome pay increase greater than 20% when only the employer's half of SS/Medicare tax is accounted for in price decreases.
Kotlikoff figures a real wage increases on the order of 19% in excess of the base income/payroll tax case.