72hr Transit Visa Issues with different Airlines for journey

Help! It appears when you are travelling to Shanghai with Singapore Airlines and Flying out within the 72 hours same airport with Swiss Air to Europe - the airline is totally confused about this 72hr Transit as not flying both legs with the same airline...Do you just fill out the normal Application Form and mark Visa "G" type on the form and submit with proof of tickets in and out of Shanghai to your state Australian office? Also do they charge you for this as I can't see any fees for a "G" on the list of fees. I tried to call the Australian offices and they state the Airline has to do it - but the Airlines don't seem to understand - they all seem very confused.