If you want as cheap as possible then you mustn't come away complaining that the GBR is rubbish. The very short trips recommended above go to the Outer Barrier Reef which will only satisfy beginners and not someone with experience. You say you are an Advanced diver but without knowing your experience it cannot be said if the Outer Barrier Reef is for you. The only way to REALLY have a quality GBR liveaboard experience is to spend the cash and get on one of the boats that does the Coral Sea (not the Outer Barrier Reef). That's where the world-class diving is. So go cheap by all means but don't have expectations that the Barrier Reef (the bit that you visit) is gonna be Great.
The OP's profile says that they have 0-24 dives, and their post says AOW. So they appear to be an inexperienced AOW diver. That's fine, and the shorter lob's that visit the outer reefs are actually likely to be appropriate in those circumstances