Can any type of op amp output stage be forced into Class A operation?
Converting a class B output stage to class A is pretty straightforward - just add a low-value resistor to one supply or the other. For instance 







simulate this circuit &ndash; Schematic created using CircuitLab

causes the internal drive level to stay positive for any output level greater than the Thevenin Equivalent voltage of the load and bypass.

It should also be pretty clear that this will dissipate considerably more power than the standard output, but that tradeoff is well-known.

It should also be noted that this may run into op amp output stage current limits. For large positive voltages, the NPN must provide much more current in the modified version, and this may not actually be possible for any particular op amp/load/bypass configuration.