After ordering a few more pairs of the 'helping hands' I dismantled the lot and had a look at what sort of components would come in useful. Turns out, nearly all of it was, and I was able to build myself some nice pieces of rigging without too much tinkering. What's extra-nice about it all is that it's fully customisable depending on the character and shape of the puppet being used. Check out a few action shots of it being used here:

Also, cleverly disguised with a bit of black cloth here: