Keep the idle time charge hidden until min mileage is reached. On reaching it add the "saved for later" charge. Causes meter to "jump" when min mileage is reached.
After min mileage is reached, idle time charge will be added to a meter instantly as it happens.
Other options:
Add to meter instantly. Regardless reaching minimum mileage or not, charge for the idle time will be added to a meter immediately.
Take from min mileage. Exchange with the equivalent amount of the minimum mileage yet left in min fare.
Throw away. Don't charge idle time until minimum mileage is fulfilled.