I use Dogtra 1900 on my shepherds, and my boy does have the longer contact points. His are the 1/2 inch I think. I don't charge mine often. I use them on walks and turn off when done and I wouldn't even say I charge weekly. If you forget to turn it off and let it sit overnight it's a big drain.
OP, I was in the exact same boat as you with my one dog who also had a perfect recall 99.99% of the time.
I had to teach him about the stim even though he hadn't disobeyed a recall because he wouldn't, the only exception being deer. And like you with the coyotes we just don't encounter them regularly and sometimes they are active, sometimes not. sometimes I swear they hide out on my land when the surrounding land is being hunted and no one hunts here.
Anyway I did him a little different than I have done most others because of how good his recall was to begin with. PM me if you want me to try and explain it to you.
Hopefully you could find a trainer that has fixed wildlife chasing with an e collar.