Thanks Kleinstein. It behaves better (less quiescent power), but is still a bit higher than expected. I have attached one circuit that I have been experimenting with. The results mostly appear to be the same as when using the TL071 model.
Perhaps this is an area where simulations are less realistic?
Simulation models always have simplifications. Most often, amplifier models do not replicate the schematic at the transistor level, but instead use ideal controlled sources to simulate basic properties. Such a model may not draw the same current from the power supply as the actual component, and an increase in output load does not necessarily result in increased power supply current. Sometimes the manufacturer writes in the file which properties the model realistically replicates, but most often it is not known.
Usually, in LTspice, I use a universal model and set the parameters that are relevant to the given application.