You have the top of the snare set at 6" or the bottom of the snare set at 6"?
I'd set the bottom of the snare from 2"-4" and the snare opening only about 4"-5" across. Possibly some smaller.
With stationary snares that require the animal to catch himself numbers are your friend. I'm talking 30-50+ snares.
The lightest wire you can stand is what you need to use.
Not sure on the wire I have as I bought a 1000
yard roll like 10 years ago and never had to worry about it since.
Rabbits are to me by far harder to catch than coons, beavers, opposums, and even
deer.
Those animals I listed tend to just push through "vines" and then flip the F out when they get caught up.
I've watched rabbits push into a snare then feel a bit of resistance then back up out of the snare just same way they came in.