@TC: Frankly I did not have the time to read the whole latest issue of the FAA book. It's online, it's free, why don't you have a look around, too? Who knows, with time we might find something.
But there is something else you might consider. About the only organisation that really does that differentiation is TC. Until now, I have not found the term power settling or settling with power other than as synonym for VRS in any other newer official publication.
What I have found so far is that almost everybody calls it VRS(SWP) - with the brackets -, even EASA, and when pilots do have the "real" SWP it is called pilot error, plain stupid or that dreaded "sudden power loss on approach" the pilot said in the accident report.
Nick Lappos once wrote that this effect was also called HTG (Hit The Ground).
From the dumb fat and happy pilot's perspective the two terms are not that far apart. From SWP/PW you can get into VRS, circumstances permitting. To solve the problem, the pilot must do the same thing - speed up, flee, get out of there, try again. Having said that, Vuichard disciples would be in for a surprise, if it was SWP and not VRS.
I personally think we should consider the following. Get rid of one of the terms, preferably SWP and never to bring it up again in any pilot handbook or publication.
It would probably save a lot of bytes in the long run. On the other hand, that would deprive us from a very funny discussion theme.