OK, I have figured this out – one way at least.
Select your source channel, press the input name block at the top left (where you can change the name and colour of the channel).
Then press Channel Library at the bottom of that dialog, press Store New, give it a name and press Apply. That will have stored the whole channel strip processing.
Now select your destination channel (you can leave the Channel Libraries dialog open), make sure your stored channel is selected in the dialog and press Recall. It will have recalled the whole channel processing into your selected channel.
It seems a little bit convoluted, but it works!
