UPDATE:
Upon taking the clutch apart, I cleaned every thing carefully with degreaser and then alcohol. I roughened the shoe friction material with emery cloth and put it all back together with plenty of wellseal on the splines, a new C27 and an o-ring inside that (mentioned in Richardson).
I put some washers under the rear pressure plate C21 against C13 as there were some significant marks in the back of it.
I evened up the lift with a couple of washers on the highest side of the lift (at the second attempt, when I realised that they need to fit over C14 too!).
On a road test today it seems much better, certain with no slip at larger throttle openings, which is a relief.
I haven’t dismissed the idea of fitting a multiplate, but certainly what I have will do for now.
Thanks all for your suggestions.
Ed.