Going straight on for motorway in middle of night (9)

I believe the answer is:

reforming

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'going straight' is the definition.
Although both the answer and definition are present participle verbs, I cannot understand how one could define the other.

'on for motorway in middle of night' is the wordplay.
'on' becomes 're' ('on' can be mean 'with reference to'**).
'motorway' becomes 'm'.
'middle of' means to look at the middle letters.
The middle letter of 'night' is 'g'.
're'+'for'+'m'+'in'+'g'='REFORMING'

Can you help me to learn more?

(Another definition for reforming that I've seen is " making things better".)

I've seen this clue in The Times.

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