If it comes down to having to chute' em' with your .22, if it helps. If you scare them in the early daylight, and set down, they'll usually be back out withing 15 minutes, if you don't move. They're wanting some breakfast. Stay still, let them come out belly down, give them a couple minutes, gun up, rested and ready, then whistle like a guinea pig, they stand up.
You can lay a blanket or a tarp and make a little tunnel for them around the trap, you want to give them a couple feet of tunnel before they walk on the wire of the trap. Best bait.....are you ready? Dirt spoils from around their hole, sprinkle a handful in the tunnel entrance, and at the back of the live trap. Scent I guess?
Also, be careful if you try dogs, I am sure the Saint Bernards would just give it one chomp, but a ground hog can mess even a coon dog up pretty bad. With a little dog if they get the upper hand, sometimes they will even pursue them a little ways (25 feet or so), vindictive or it's like they want to make the message clear. Don't get me wrong, there are smaller natural "coursing" dogs that know how to handle them. Some black labs seem to be good "groundhog dogs".
Good luck, the cayenne should deter it. Also, I don't think a little cayenne will hurt you chickens. I have one hen in particular that likes to jump down inside my compost barrels, I had to start burying my really hot pepper seeds. She'd vanish into the drum, then you'd see her pop back up, shaking her head going "pft pft", and then right back down to do it all again. Funny, but I started covering them.