Over the weekend I re-recorded the affected tracks using Garageband, using the same levels, parameters, etc. I imported the song into Logic, exported it again as audio files and there was not even a hint of distortion, so I'm guessing the original files had somehow got corrupted. I also recorded the tracks again, this time using Logic, and exported them with same distortion free result.
I'm new to Logic so I really appreciate you taking time out to help. Many thanks. Oh, by the way, any tips you can give on Logic's noise-correction tools would be greatly appreciated.
Once again, many thanks.