Crossword Genius

What that drink over the eight did, as one went towards (4,4,3)

Ross

I believe the answer is:

made ones way

I'm a little stuck... Click here to teach me more about this clue!

'went towards' is the definition.
I know nothing about this answer so I can't judge whether it can be defined by this definition.

'what that drink over the eight did as one' is the wordplay.
I cannot quite understand how this works, but
'drink' could be 'ade' (I've seen this in another clue) and 'ade' is located in the answer.
'over' could be 'on' (physically on top of) and 'on' is found in the answer.
'one' could be 'me' (a setter might use 'one' to humourously mean 'me') and 'me' is located in the remaining letters.
The remaining letters 'sway' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

I've seen this clue in the Evening Standard.
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