You should expect the fare to be doubled to compensate for the empty return trip. For those on TDY to Camp Zama, the probability of reimbursement for taxi fares to either downtown Tokyo or Camp Zama is doubtful in view of the availability of less costly modes, i.e., bus or train. The MWR bus goes to Yokota AB via the New Sanno Hotel in downtown Tokyo. Pets may also be shipped as commercial cargo to arrive to Narita. Shipment of pets must be at the owner's expense whether moving as excess baggage or commercial cargo.
Excess baggage is usually the cheaper of the two.
It is extremely important that required documentation is in order.