I have a Thule Cougar trailer and I would love to put these Burley fat tire wheels on it. Because reasons. The push button hubs on the Burley wheels look the same as the ones used on my Thule, but I can't find a definitive answer on compatibility.
For anyone still searching the internet for a definitive answer to this question, I have one!
The Burley axle is indeed just a hair too long, but at the same time too short. The plastic brake housing extends past the bearing on the Burley version whereas the Chariot is close to flush. The two brands are annoyingly similar but just different enough - same axle diameter, same bearings, same brake layout, close to the same axle length, and 10 spokes vs 12. I pulled apart both sets of wheels trying to get a solution that wasn't destructive. In the end, the easiest (and cheapest) answer is to cut, sand, or otherwise trim down the Burley brake housing about 3/16". If you do that, the Burley fat wheels will work perfectly, even the brake. What's left of the housing will act as the bushing against the trailer body so the more you sand down the hub beyond when it connects, the more horizontal travel you'll have on the axle. Not a problem, just a minor annoyance if you're picky.
Photos here: https://photos.app.goo.gl/4QwgkM5UqLPa7rq16
Got a reply from a dual owner (burley and Thule) that they have a slightly different axle-witdh (should have been thickness). :( https://thismombikes.net/child-trailers-chariot-vs-burley/