Thanks to everyone who helped me out with thoughts and suggestions about my 'pig tail' plying issues. I think I know where I'm going wrong! The main problem seems to be the lack of tension on the spool I am plying from. Too much yarn comes out at once, and it twists back on itself. So I need to play around with that some more.
One friend suggested that I practice plying with store bought yarn rather than my hand spun. That made perfect sense to me. So much time and effort goes into producing a spool of hand spun, it seems a shame to mess it up 'practising' your plying technique.
Of course, I don't actually do the 'store bought' yarn thing... but I do have a plentiful supply of yarn here, which would actually benefit from being plyed. Especially some of the cottons I have reclaimed. So I will definitely give that a go.
In the meantime, I had a play with plying one strand of handspun with one strand of reclaimed yarn. I love these colours together.