I was worried about the same thing too before I left, whether we'd be stuck with nothing at all... but I decided to take a risk and wait anyway... at the supposed HEIGHT of the dive season at GBR (May/June). When we got there, not only did ALL of the live-aboards have vacancies but they were so much cheaper than the prices advertised online.
There were 18 out of 28 spots filled on the boat I went on, and that was late May, early June. With so many live-aboard options and travelling traffic at a low, I'd wait... I highly doubt all decent live-aboards going up north will be full. Especially since you're on a budget, you'll find much better deals. For price value, Taka and Spirit of Freedom were the cheapest that are going out to the northern reefs and/or coral sea. Taka has a 5 day Coral Sea/Cod Hole trip for $550 AUD(when you book it there), and Spirit of Freedom has a 4 day Cod Hole/Ribbon Reefs trip for $750(when you book there). The Spirit of Freedom is a much nicer boat than the Taka, and a guy I met there that went on the Taka boat said it was a barf fest... but I guess that really depends on the conditions, the seas were a little on the rougher side when we went.
There are much cheaper live-aboards in Cairns, but they all go to the closer mass frequented spots. When are you thinking of going? If money is not a problem, maybe you'd be better off booking ahead, just for peace of mind. The money I saved allowed me to leave a nice tip and paid for 5 days worth of lodging at a hostel. Every dive shop and tour group there can book you on any of the live-aboards, so walk around town and explore the options and pricing. The deals I mentioned were computer print-outs posted on walls in the tour agencies and dive shops, so it seemed like a normal deal type thing... you could probably get a better rate, if you really wanted to... I was too excited about the trip and price and booked it pretty quick. So I personally would wait, we did the trip in May/June of this year, I have no idea what it is at other times of the year.