You could try slug nematodes. These are parasites of slugs that can kill them. They occur normally in the soil, but their numbers are normally in balance with the slug population. The trick is to increase the number of nematodes to the point where the slug population collapses. The problem is that this causes the netmatodes' source of food to vanish, so the nematode population then also dips until the slug population recovers. Thus to keep the slug population down, you need to keep the nematode population higher than normal by periodically re-applying the nematodes.
Nematodes can be bought online, or made at home. When bought online, they are delivered in a sachet that must be kept refrigerated on receipt, or used immediately. To spread on the garden: mix with water and spread over the garden.
You may be able to make slug nematodes at home by collecting slugs, keeping them captive in a watered container, feeding them and allowing them to die. The resulting mush can be watered into the garden. More here:
You could also try a hybrid solution: buy them online, keep a slug nursery that you apply some of the nematodes to. Keep feeding the nursery with caught slugs (beer traps?) and keep decanting the water to reapply to the garden. This would be my choice.
You must keep the soil moist for a while after spreading, or the nematodes die before they have a chance to infect the slugs. In the past, I have been a bit erratic at watering as we do not have a hose, just watering cans. Thus, when I have (twice now) spread commercially bought nematodes, there was an immediate dry hot spell that killed off both slugs and nematodes and it is hard to gauge how well they worked. I mean to install a drip-irrigation system that will, together with appropriate mulching, help with irrigation. Then I will reattempt my nematode experiment, perhaps in two different parts of the garden (they are divided by a wall) and I may well report back here. Don't hold your breath though :-)