Slugs in my compost
You are right not to add slug pellets to your compost as these can kill the organisms that actually carry out the composting process.
Slugs love compost bins and they can provide an ideal breeding ground for them. However, because the compost bin is such a haven for them, they are quite happy living there and therefore are not interested in heading further afield to your plants and veg. In this respect they shouldn’t prove a problem in your garden. Slugs are part of the process of compost making – they play a part in breaking down the material. Many people actually throw slugs they find in the garden onto the compost heap/bin as they are beneficial there!
I appreciate that they are not very nice (make my flesh creep!) and understand why you might not want them there. If picking them out is not an option, you could try applying nemaslug to your compost heap. This targets only slugs, so should leave the other beneficial organisms alone. This needs to be applied every 6 weeks to moist soil/compost. This will work on soil, but not on fresh material in the compost bin.
Good luck with your slug eradication. Please let me know if you need any further help.