Well, I decided to buy a live trap (and then figure out how to dispatch the critters after). I got the trap yesterday and set it up with PB, some chocolate flavored almonds, and some old stale Trader Joes truffle 'cheetoes' lol. Within 4 hours, this was the result:

What's strange is that the poor guy was already dead so I'm really not sure what happened. I have a couple theories:
1) it was stuck in there for a long time (possibly went right in shortly after I set the trap) and died of dehydration after a couple hours of being stuck.
or
2) a hawk came over and started toying with it and eventually got its claws on it. I didn't see any blood or signs of struggle but you never know.
Anyway, I tossed the carcass over our fence and into the shrubs/bushes on the hillside. Hopefully a scavenger was able to pick it up. This morning, coincidentally, I saw a hawk perched on our fence which was really cool! Wondering if this whole ordeal possibly drew him back to "patrol" our yard.
Re the trap: I wasn't checking the thing every 15-30 minutes since this was in the middle of the work day. I figured it would take a while for anything to get caught so assumed it would be fine just to wait and leave it out there. I guess I should have set a camera up to monitor it. I'll probably do that from now on.
On a related note, an idea crossed my mind as an alternative to a pellet gun: Mini Crossbow! There are some that can be had for $50-80 on Amazon. This seems like a great solution for something quiet and that wouldn't really ricochet, while still being accurate and deadly. I want to see how this trapping effort goes though. I may try the bucket/water/sunflower seed trick too at some point. For the time being though, I'd just like to try to get them under control a bit. They are stealing the apples of our crab apple tree as well. It would be nice to enjoy the fruits from our yard. I don't want to imagine what these guys would do to new young plants that we're just trying to establish and paid a bunch of money for.