Crossword Genius

Criminal beds lad with a thousand rolls of fat (9)

Ross

I believe the answer is:

saddlebag

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'rolls of fat' is the definition.
Although both the answer and definition are singular nouns, I can't understand how one could define the other.

'criminal beds lad with a thousand' is the wordplay.
'criminal' is an anagram indicator.
'with' says to put letters next to each other.
'thousand' becomes 'g' (synonyms).
'beds'+'lad'='bedslad'
'bedslad' is an anagram of 'saddleb'.
'saddleb'+'a'+'g'='SADDLEBAG'

Can you help me to learn more?

(Other definitions for saddlebag that I've seen before include "storage place for bicycles" , "Rider's large carrier" , "Rider's pouch" , "Attachment to bike" , "It's attached behind on a bike" .)

I've seen this clue in The Independent.
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