This is an excellent puzzle, and well worth some head-scratching.
The thematic phrase and instructions from the omitted/extra letters, the two quotations and the symmetry in the completed grid all help each other. If the setter believed the puzzle to be unsolvable without more information, the preamble would have given some. It doesn't. The puzzle is there to be solved as it stands.
Nobody is expected to complete this type of puzzle in ten minutes flat. It's a Listener. It's not meant to be easy - persistence and doggedness are required.
The closing date is still over a week away, and for those not planning on submitting an entry no time limit exists. Three semi-lucky people will receive a dictionary for their efforts (currently available for only £20 on Amazon) but nobody else will get anything at all, not even a pat on the back from their mates. They may award themselves some kudos from having 'beaten' the setter, but those who've had a leg-up along the way are fooling nobody but themselves.
Here's a thought: maybe someone should write to the Listener editors, suggesting that the solution be printed alongside the puzzle, for the sake of those who can't be bothered to think.
Happy New Year.