Maybe if two regiments really want a ref for their match, they should be allowed to find a neutral one on their own who they both agree upon. That way the organizers of the league don't get hassled with all that stuff. But then the regiments have to completely trust the ref's decisions, even if they think they're wrong etc.(just like in football)...After the match the ref just tells the league organizers the score, end of discussion.
For regiments that don't need a ref, or can't find a ref, nothing changes to now.