Shed on island given to family for Jack Straw? (9)

I believe the answer is:

spillikin

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'jack straw?' is the definition.
The definition suggests a singular noun which matches the answer.

'shed on island given to family' is the wordplay.
'shed' becomes 'spill' (I've seen this before).
'on' is a charade indicator (letters next to each other).
'island' becomes 'i'.
'given to' means one lot of letters go next to another.
'family' becomes 'kin' (synonyms).
'spill'+'i'+'kin'='SPILLIKIN'

'for' acts as a link.

Can you help me to learn more?

(Another definition for spillikin that I've seen is " Jackstraw".)

I've seen this clue in The Guardian.

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