Multi-partying is now an issue

Well there are a couple of ways one could go about this. For starters if people are friends, don't dump them into the same matches unless they are on the same team. Another potential solution, suspend accounts of people caught doing it. First offense a 1 week suspension, second offense a 1 month suspension, third offense 6 months and 4th 1 year suspension. Hand out the suspension across all EA games, not just Apex Legends. That would make people knock it off real quick, but I'm a firm believer in harsh punishments for bad behavior.

Depending on how long it takes the game to generate matches.. queue timers. When a team presses the queue button, it randomly picks a  time between .01 seconds and 59 seconds before it actually starts looking for a match. One team would get let's say 10 seconds before it actively looks for a match, while another would get  40 seconds before it looks for a match. This would help get them into different matches. If new matches are generated every 10 seconds then set it so the times are at least 10 seconds apart. 

This way if you have two teams press Y at close to the same time they will end up in different matches most of the time. 1 might get a queue timer of 10 seconds, while the other 30 seconds. The team with the 10 second timer will go into match before the team with the 30 second timer.

Do away with the "here is your champion" page. That makes it easy to identify if you're on the same map. But I'm not sure how effective that would be, you can still identify it based on the flight path of the drop ship, the landing location of the ship with loot and the hot zone.