Beer traps are really good and kill lots. Dusk patrols are worthwhile – going out with a torch and collecting all the slugs which can be put in a bucket of weak beer solution. A couple of years ago we were getting at least 100 per evening and it made a difference.
It’s also worth looking at the causes of the high population of slugs – is there long grass or other hiding places near the veg plot?
Very glad to hear your son doesn’t want to use slug pellets, I work for a wildlife hospital and it’s devastating to see what those things can do to hedgehogs.