I was not the only one. Edward Aveyard writes
I noticed your recent post on whether the Queen really uses /ai/ for MOUTH or not. If you listen from 3:40 to the Christmas message, she says “countless thousands”. I hear aʊ in countless but aɨ in thousands. … It's almost as if she had been reading your blog and wanted to give you something to analyse.
On Christmas Day I tried to download the video of the speech from the BBC website, but without success: although you could watch it you couldn’t save it. I looked on YouTube, but it wasn’t there. Now, though, TheRoyalChannel has uploaded it to YouTube: thanks, Edward, for the link.
Listen here, at 03:45, for the phrase in question.
I agree with Edward’s judgment. Watch HM’s lips in each of the two MOUTH tokens.
Another interesting pronunciation is powerful, here at 03:17.
It appears to be fully smoothed and compressed, ˈpaːfl̩. This is how I often pronounce that word myself, though some people seem disinclined to believe me when I assert that this reduction is widespread in RP. In my analysis, the “smoothing” process removes the second element of a diphthong, in this case MOUTH, when before another vowel (aʊ ə → a ə — or, of course, it could equally well have been aɨ ə → a ə). Then the “compression” process reduces two syllables to one (a.ə → aə). Finally, the monophthongization process suppresses the second element of the resulting diphthong, with compensatory lengthening of the first element (aə → aː). Thus a possible ˈpaʊ əf l̩ is reduced to ˈpaːf l̩. All three processes are variable (optional) and rule-governed (systematic).
There was a Two Ronnies sketch about misunderstandings arising from PRICE-MOUTH confusion (ground misheard as grind, etc). Can anyone locate it on YouTube or elsewhere?