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Aha, so correcting my wrong second word in 1a was the key to solving both 5d and 6d for me.

No hints needed anymore (although I'm not sure I can parse how either clue 5d or clue 6d works).

But I think this puzzle is indeed cognizant of its being the 300th puzzle in this series, because of the theme visible at 1a, 4d, 25a.

15d - I have no idea what I’m doing.

Is WAY = ST?

Hi Druh,

No, it often is but not this instance. The "way up" refers to how one gets from the bottom of the Alps to the top when on a skiing trip.

The latest Guardian blog discusses the Times solving competition, which this year included an AI dog.
It suggests that AI can’t process humour because it can only understand something it has seen before.
This clue seems like the sort of clue AI couldn’t comprehend (for now).

Thank you. The slog continues!

Out of curiosity, are you the same Brendan that sets some of the Guardian crosswords?

… the dog lost by the way.

Thanks Druh and, if it makes you feel any better, I thought this was a particularly difficult Everyman, so hats off for sticking with it:-)

No, that's another much more talented Brendan.

20a - Baddies at home, inhabiting country houses (8)

Is HOME = IN/INN?

“At home” = IN.
This is often used, so worth remembering.
The other part of the answer is a word for country houses.