The spec sheet for the LM323 says it should get a minimum of 7.5V in, but that 8V supply should be reduced to 6.6V after it's gone through the bridge.
Are you sure you're getting good regulation out of the LM723?
Also, it looks like the ripple on the filtered DC could get pretty awful as you start to load down the supply with AC input, due to the relatively small size of the capacitor. The problem you saw running off the transformer might not have been "wimping out": it could well have been the LM723 dropping in and out of regulation because its input voltage was swinging too widely.
Iit's a rather nasty combination: as the current goes up, the average DC voltage goes down, and the swings get wider.
Feeding it regulated DC is a clever way to avoid that, but I wonder if it shouldn't be 9V, instead of 8V.