This system probably won't work at all, because the only way for randoms would be up. What could happen though is to weight wins and losses accordingly. However, if you already have discovered the needed weight to make it fair, you can just set up a proper match up in the first place (i.e. lower skill arranged team vs higher skill randoms). They should have tons of data of CoH2 to make a decent guess for CoH3, how much stronger an arranged team is, just because they are "arranged" and not random.
There is no way to achieve "fairness" in randoms vs arranged. It is inherently massively unfair no matter the player skill involved. It should not effect a competitive ladder whatsoever. I honestly don't care if this leads to massive drops at the start. Random teams should not have to fight arranged (if they don't want to).
Also, metas come and go, at times you can have severely cancerous synergizing metas dominating that will skew things even farther in the direction of arranged vs random, IE the current state of 4v4 with pathfinder shit.