Used a length of grey pipe insulation foam tubing with a suitable wedge cut out for the top edge of the stock. Have tried different attachment methods, some not great for the varnish. Hot melt glue blobs not bad as peel off OK. The bare foam is very light, but especially if you have cheek stubble it's crackling in your ears.
Next time I'm going for the shell holder thingamebob suggested by @kidmac42, maybe still with piece of foam riding on the top edge of the stock.
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