Thanks to the help received here, my stage monitor is now working properly. As recommended, power pins decoupled at the ICs, 100 ohm resistors fitted to isolate the output pin from stray capacitance to ground. I did manage to borrow a 'scope, and even after applying the remedies it was clear that crossover distortion was still present - it looked on the screen just like the drawings in the text books. Well, I s'pose it would really, wouldn't it!!
It all went away after replacing the LM358 with a TL082 in both parts of the circuit. It now sounds sweeeeeeeet !!!! Thanks to all - but especially Phil Allison and Eeyore - for the good advice.