You could try planting a border of slug repellant plants, and a couple of plants the slugs like more than your crops, once a week you just pick the slugs off and drop em in a bucket or water or something.
Quick google-fu suggests the best non toxic chemical slug solutions are crushed eggshells or coffee grounds (the caffine is the key, also brew some coffee dilute it and spray it on your worst affected plants).
As repellent you could try garlic and rosemary, other kinds of highly aromatic herbs should be possible, a bit more googling should find more, also if you have herbs already just plant more of whatever they don't seem to be attacking.
And as i suggested take whatever plants they seem to love the most and plant a few off to the side a few meters away from your main crops, wait for it to be overrun and spray emn with whatever works, just let the plant take one for the team and attract them away to be killed.
Also, you might try different plants altogether, or different varieties of the same plant, not all species have the same chemical warfare capabilities, one again google should help find slug resistant varieties, or just plant several different kinds together and keep whatever seems strongest.
Now an update for harvest Dwarf Real life edition; Bed 1 is now ready for planting, the plan is to place 2-3 month maturing crops there next to the fence (where the bananas were supposed to stay) whilst allowing the bed in front which is now overrun with bananas to compost for the same amount of time, by the end of september that bed should be ready for more nutrient intensive crops that'll prefer full sunlight, the youngest banana shoots will be moved to the back where they should belong (as long as i dont ignore them for 5 years again).
I just need to get the chicken proofing done and then plant.