Trapped in Northern Australia

Guess what? There are holidays in the middle of December! Who knew! That's right, Australia takes off and leaves from around mid-December to end of January. The airlines figured this out before me and know they can charge stupid amounts for normally cheap airfares. For instance, Darwin to Singpapore on Jetstar is often $50 to $100, but during this season it ranges from $300 and up. Not only that, but I'd much rather get to Bangkok, since there are cheaper flights from there to Kolkata, India, which is where I think I'll start my tour there, but there are no flights on the cheap airlines from Darwin to Bangkok. Vayama and a few other services come up with amazing routes taking me to Cairns, to Sydney, and then back up to Singapore, which is absurd. Flights from Cairns aren't cheap either. Options are to leave Australia ASAP, which I don't want to do, or extend my visa for $100. But first, I need to escape Exmouth. There's a bus that comes through, with a transfer, at a stupid hour in the middle of the night and involves a scary number of hours to get to Broome, from which I still need to move on to the next destination. I can get a ride to Port Hedland, but then I'd be stuck there for 4 days waiting for the bus. There is nothing to do in Port Hedland. Hmm.