1x19 does make a much nicer loop, but its the closing speed of 7x7 that I like.
Archer refered to "loading" snares. To do this, take an open snare and pull the first 6-8" of cable between your finger and your thumb a few times. This will help round out your loop, but don't expect a perfect circle with 7x7. I use a 17ga support wire that I wrap around the top portion of my snare that enables me to set the pitch of the loaded portion.
I don't know what regulations your state is under, but an 8"ish diameter loop that is 6-7" off the ground is not
a coyote setup. Your coyotes are hitting your snares with their chest and carrying on. General rule of thumb is 10-12" diameter loop and 10-12" off the ground. Your way further ahead with a higher loop and a suttle chin up stick than trying to make a coyote duck down.
That short tension spring you mentioned, is it a dispatch spring? If so, you will likely need a support wire to help with the extra weight.