It sounds a lot like our league. We’re all self group scoring, and then our League President is always present (or someone he deputizes for the night if he’s not) to handle any rulings and malfunctions that come up.
And yes . . the language is ambiguous on purpose so it’s easier for me to just say “NO” to most people, instead of being explicit, and having people try and probe for workarounds anyway
Thanks to some help from Keefer he was able to find a website that showed the average number of balls thrown based on your finishing score. I’m okay with following something like this, but will deal with those that want to run Pin-Bowling, or gasp, Pin-Duck-Bowling (the better version) on a case by case basis. It’s been pretty rare up to this point.