I'd agree that day trips from Cairns just really pale in comparison to the outer reefs. Unfortunately LOBs (as unfortunately all diving in Aus), is incredibly expensive. A compromise may be a shorter trip, perhaps? Mike Ball, which I've done, and others already mentioned here (Spirit of Freedom, Taka) do do shorter trips of 3-4 days, so not quite as expensive but you still get to the otuer reefs.
If you do the Yongala, I'd really recommend going from Airlie Beach rather than Townsville. From Townsville it's a much longer sail..and for that reason the seas can be much rougher and it gets frequently cancelled (I've learned the hard way). From Airlie Beach it's much closer and they often go out on days the trips from Townsville are cancelled.
Taka no longer does the Cod Hole / Osprey trip. It still acts as a liveabaord but is stationed on Norman / Saxon reef there are daily transfers with the Divers Den dayboat from Cairns. Shame as it was a good budget option to get to Osprey.
Re: the Yongala, the quick trip actually runs from Alva Beach, 16km out of Ayr. I'm pretty sure no operators run from Airlie, and if they did it would take even longer than from Townsville.