You're exactly right, we do have weird ball valves. Maybe not weird, just different. The ball valves are like the poster below said, polarity sensing. I should have made that clear in my original post.

If you have Tee-Jet valves that have an E somewhere in the model number it's my understanding that they are polarity sensing ball valves. We're seriously thinking about following the next posters advice and just getting rid of them. It looks like we're going to have to get creative any way we do it but that may be the one that requires the least amount of effort.