One thing for us to consider: do we want to limit speedruns in any way to just the characters you can get via the story or via tickets? (That is, right now: not Squall or Cloud.)
We could always create an "all characters" mode but if SE is going to make it so you can't ever get these characters again it could put a damper on speedrunning it if they turn out to be particularly good.
Luckily Cloud and squall (currently) are terrible. They’ve also stated in their twitter update they will likely return in the future to account for people that missed them. In what manner though is unknown. They can’t be used in regular story mode anyway, just extra mode. Based on experience there’s no instance either of the current characters would ever be a good choice in any speed related race.
I think maybe by next season pass, depending on how they handle the release, we will have a better understanding of how to classify the rules. They may make them both obtainable with gil and not lock one behind mythril, or even make them permanently available with gil. For now, I guess it is best to not allow cloud specifically for any of the leaderboards, but squall should be fine since he is easily obtained with gil. If squall dissappears and never returns, and receives a buff that makes him really good, then the boards should be split as you described. Just my opinion though. (Cloud is honestly one of the worst in the game though, his ability is bottom tier… in need of a buff)