Wow..that sounds like lot of ..'fun'. I've done my fair share of snail hunting during night myself in past..but there is no short cuts for the trouble...just hard work and you will get top of it.
There is 'millions' of way of trap them..but if you have that quantity of them to start with traps are not going to make much difference..as soon as you set them on..they'll be filled up and useless again.
I think most effective thing in your situation and any new land area that is taken to veg cultivation is to give it a double doze of nematodes. One in the begining of the growing season and other in couple of months time.
You can purchase these nematoded over internet from many companies..you will receive packet of 'powder' where there is live microscopic predatory nematodes that you mix with water and you water them in into moist soil where they immediately start looking their new 'homes'..they get inside the slugs and snails resulting all the slimy's being eaten inside out. They are not harmful for the wild life..nor they will live forever in your soil..once the soil conditions change and/or food source run out, nematodes will die out too. They won't have effect to any snail eggs that are in soil..so repeat treatment will ensure all the newly hatched ones get busted too.
These treatment are not cheap..around £15-20 per treatment..but applied by the instructions and given the soil conditions are right, it is most effective treatment around.
I found double treatment was enough for my situation and after that I've managed to keep those things under control with other measures...like having couple of small wildlife ponds, feeding wildbirds (I've got loooads of visitors and permanent residents), hedgehogs and pair of sturdy size 7 wellies for snails..and chickens will finish the resulting 'mush' quite happily.
It will take few years to attract enough wildlife for you to be able to stand back and let them deal with the pests..but it is do-able.