Oh dear. I misremembered and may have misled yesterday evening when I said that both words I have for 29 down are in Chambers. One of them is there but I actually got them from Word Wizard and confirmed the other one by googling it.
piffleworthy (# 6), one of the regular beefs raised here about the Spectator crosswords is that, apart from when we’re being steered in the direction of, say, Brewer or the ODQ, there’s usually no indication of the principal reference work. I found 17 down on Word Wizard and, like you, also found it in Collins.
Thank you, the18racer, for that arcane bit of specialised info about 15 down.
peterm, I agree that this is not one of Doc’s best. Not for the first time with this sort of puzzle, I lack confidence that the set of unclued words he has come up with is definitive and that there are no alternatives.