Chill the beer, then rack it to the keg. Purge with CO2, then "burst carb" (shake the keg for 5-10 minutes while applying 10-12 psi of CO2). Drop pressure back down to 5 psi and purge excess. Bottle the entire batch with your beer gun. Once the keg is empty, clean it, and repeat with the next batch.
Note that the beer has to be cold before starting.
If you're worried about overcarbing, and you've got time, instead of shaking the keg, you could just put it in the fridge under about 30 psi of CO2 for 24-36 hours (check it every few hours near the end to make sure you don't over-carb), then once the carb is where you want it, drop the pressure down to 5 psi, vent the keg, and bottle as described before. Repeat for the next batch.