A tournament would do that. The only problem is that some would go against relatively strong competitors to start off with. It's still a huge improvement. You would still have some randomization of the result based on who they faced along the way.
One somewhat flawed method to address this would be to find additional methods to estimate strength and then match the stronger half against the weaker half. Then those who were going to make it to the second round anyway will also have faced a more narrow range of difficulty to get there. But if your alternate methods are less than perfect then you are biasing the results towards those methods. And if they were perfect there would be no need for the elimination process. So then what you really need are really good methods for predicting strength and then you use the tournament as a sanity check.
The method used is obviously flawed, as it does not account for wear in M&M's that are selected early in the process. Instead efforts should be made to ensure that all contestants take part in about the same number of contests.