Using traps live and fenns is good, but you will find it hard to get full control without poisons.
Secondary poisoning is an issue but if you bait underground i.e. burrow baiting, most dead will remain underground.
Bait and block off as many burrows as poss and keep a very close eye on pets, opened burrows and for bodies.
What about external preasure from surrounding rodent colonies? Do you know where they are coming from, could it be outside of your control?
Best of luck!