Hi,I tweaked the amplifier so that its output swing is much more than before. 0.86W output at low distortion.
The theoretical maximum efficiency is pi/4 but did you try to use a symmetrical drive in the manner in which you used for the upper stage? I would think that would boost the efficiency even more as it does with MOSFETs.
The bootstrap idea works with MOSFETs also and in fact that provides a lot better performance with those transistors because of the usual gate source voltage requirements.
See if that helps.