Elections aren't fraudulent just because you don't like how they're conducted. I can think of good reasons why orgs would structure elections in that way. Only counting votes from people present prevents absenteeism, and no voter anonmymity means that people are responsible for the fallout of their choices. Note that there are certainly counterarguments for each of these points, but there are nonetheless good reasons to have elections like this. Elections in orgs don't have to directly mirror elections in your state to be considered valid, and in fact, they probably shouldn't.
As others have said, most anarchist orgs don't really have elections as such. The organization attempts to reach consensus with a few conditions, and if consensus isn't reached, those that dislike the outcome just won't participate or will leave and start their own org.

This left thing that you're in sounds like it's not explicitly anarchist, but it's hard to be sure from what you've said. If it's not anarchist, then I guess your choices are to play by their rules, or leave and form an explicitly anarchist chapter that does something similar. Although I should note that playing by their rules isn't necessarily a bad thing. I'm in plenty of leftist orgs who I'm not in 100% ideological agreememt with because they do good work. You've got to decide whether splitting is worth it or whether it's better to maintain unity.