If efficiency is a concern, there are surely modern Class D headphone amp chips that are much better than LM386 (my goodness is that thing old, it should have gone into management years ago). They're not the audio quality of the above chip, but depending on your application they might still be plenty good enough.
OP, please state:
* supply voltage (min/max)
* load impedance
* required gain
and perhaps acceptable idle current draw.
DIP could be a problem indeed. The crummy old LM386 noise and distortion generator is the very last thing I would use for sure.
An opamp + power buffer concept may potentially be more promising. (Power amp chips are not uncommonly built to be operated at low inverting gain following an opamp output these days.) There is always something you can do given enough PCB real estate or power.
I haven't used LM4871, but I'll probably get some the next time I order parts. I like the ease of use of the LM380 / LM386 chips, so I still use them. Hard to beat for hobby use, imo. Probably why they still make them in DIP.