I think people who have issue with triggerring Barrel's stuff will have issue triggering the wrestling event with him too. I've heard this advice before, but it doesn't work for me, Barrel just doesn't show up for wrestling. It's something that happens earlier that obstructs him from ever appearing in Bareshade again (tbf Barell has also never even crashed at my place either)
In order for all of event with Barrel to trigger you need to have Bandit camp morale over 20 for him to start showing off at bareshade which include wrestling and all other events, to get bandit morale up go to Bandit camp and give money to Jester to increase it 3 times a day, and be warned that bandit morale decreases daily, so you need to keep it up if you want them to show up