Yes... deadfalls and spring-up traps do work.
But for serious meat-getting with the least time and effort your current snares are as good as anything in my opinion.
Wire snares are strong, and they are very convenient to use in that they hold their shape. Because they are relatively stiff, they stay open in position without having to go to a lot of trouble to support them.
However, in my experience at least, once you've caught a critter in a wire snare, chances are the snare will be kinked which will make it harder to set next time.
I've trapped hundreds of animals in home-made snares, most of them made from synthetic cord. I like using nylon braid because it has a shock-absorbing stretch factor. I've had very few break-offs or chew-offs. And I generally always use a simple running noose with no form of lock. I figure that if the animal breaks the tether, then he has a chance of shedding the snare fairly soon. If the animal got a way with a locked snare around its neck, life could be uncomfortable.
Deadfalls and spring-ups are good traps to understand. If you don't have decent cordage for snares, then they are a good option. You don't need any cordage for certain deadfall traps. And when a critter is held in a spring-up, it cant get much traction on the ground... and it can be harder for it to turn and chew the cord. So I believe you can get away with using relatively weak cord for your spring-up snare. Also the spring mechanism helps to reduce sudden shock loads on the snare.
Where a snared animal is likely to be eaten by a scavenger before the trapper gets to it, then it could be a good idea to have a spring-up that lifts the trapped animal out of reach. I've never had to do this in my neighborhood.
Deadfalls are particularly good for rodents. I've caught lots of rats and mice using a figure-four trigger.
Best wishes from New Zealand.
