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For completeness, I'd like to know how 7 works. The answer is obvious enough, and surely 'F' is the extra letter (?). Similarly, I've not parsed 19, though again the answer is straightforward. This was better than the last 4 or 5 puzzles, to my mind...

For 7, the extra letter is T. It's a 4-letter word for a film or web around (T)EG. 19 is ER(R) around a time period.

The only one I haven't figured out is 23. I have the answer and the extra letter, but I don't know how the last four words in the clue work to produce the end of the answer.

c = speed of light

I'm still no further on with top left corner. Hints for 9ac and 11d would be helpful. Also, I don't get why the R has moved in 5ac, and the reason for the last four letters in 5d - why are they a small office? Thanks

5ac CRAT(E)ON and for 5dn a LAV is a shortened form of lavatory which Chambers says can be an office!

9ac the summons is a reveille and in 11dn the reminder is a prod.

9a is a French expression; the word for 'summons' is in Bradford's - think military camp; 'Duck' refers to the setter, not O.
11d - a standard 6-letter word for sailor following a 4-letter word for 'reminder' (giving an extra letter).
The R hasn't moved in 5a - perhaps you have the wrong answer.
5d - Look up 'office' in Chambers. 'Small' in the clue indicates an abbreviation.

Thanks Jaye. Having resolved my difficulty in 7, you've created another for me, that is to understand the hint. I'd been pretty set on 'RATIFY...' from the down clues.

Meursault, I suspect you have chosen the wrong extra letter for the last across clue. There are three possibilities. The second part of the message starts at the last across clue

Perhaps I should add that there are also two possibilities for the extra letter from 5d, and you have the wrong one.