Hi Neil,
attached photo's showing method.
Open my drawing and in browser show curves so you can use them.
Please note the head & base profiles have been rebuilt using the rebuild command.
This gives a continuous joined curve with only one seam line.
(You can have issues when filleting across seams and edges.)
To achieve this there can be no sharp corners so use a small fillet to remove them.
Also have you got the show naked edges script as this would help to see the areas
that are stopping the joined surface from becoming a solid.
Hope this helps.
Barry