Class A, no feedback, 5W, minimum parts

In which thread?
Well, you asked about the 4W-amp right, then it´s probably in the thread about the 4W-amp ;-)
The link is in post #8 in case you forgot.

If you, for whatever reason, are looking for a Class-A buffer that you can drive with your headphone amp (assuming that has some voltage gain), you could have a look at this FET-buffer which gets some love around here:
SEWA - Seven Watt Amplifier
But that one has considerable power dissipation for little output; just saying.
 
I have an RME Babyface Pro, which the engineers have assured me can swing 8.4V into as little as 600 ohms (line level, one side of the balanced output - both sides too).

That design looks like it does exactly what I'm looking for. 7v rms (10v p-p). Is it just the one 40V rail? I'm not concerned about efficiency. My last amp (if I can't get it fixed) was a 140 (more like 250) watt into 8 ohms (1000 into one, single channel only - 32A) which pulled 370 watts/500something VA in normal use.

I came across another design, simpler with no voltage gain, called the "mofo" lol. Have you heard of it? Apparently people were impressed

https://www.diyaudio.com/forums/pass-labs/313649-build-mofo-279.html#post6368030