The trammel is going to hold well but I could not get a rabbit out of that on a black night, definitely not in a rush.
As for bouncing on a quickest or trad net a 4z is a good start, as tommo said you want to trot the rabbit in to tangle but mesh size is also important. I would no longer entertain a 4 inch mesh. Others will and do and that is their choice but I like 4.25.
if the head goes through the mesh it wont be bouncing as often. I find they try to push on..