I think I've been able to adjust my mindset to making this work.
Which is another way of saying I was being an idiot.
The reason hidden shares are called hidden is because they are hidden, which means they can't be found. The clue is in the name. So the error message is OSX's way of saying "I can't find any shares on that machine."
I'd still rather it had said "I can't find any shares on that machine" instead of "The alias ... could not be opened because the original item cannot be found", which is slightly misleading. I actually thought there was a bigger problem than that it couldn't find any shares; it had that sort of feel to it.
Now I have set up visible shares (ie. with names not ending in '$') they are easily clickable and all is bliss.
Do you know if there's an easy way of asking the machine to try and reconnect an SMB share at startup? (And preferably not sulk for too long if it can't.)