WOW!!! I am so sorry that you are going through this right now.
Can I mention an important point? You mentioned "petting zoo". One thing I would recommend is to stop all hand to rabbit contact for a bit, at least until you know what is going on. You can spread something if you are going cage to cage touching each rabbit. Its very hard........I know!! We also keep a hand sanitizing gel in the rabbitry, right in an easy access point.
I have a hubs who put up similar resistance, but unlike yours, it's just because he didn't want to deal with it. I was met with resistance along every step of the way, initially with quarantining, then building the rabbitry, and what we needed to do in the rabbitry, as well as sneezing and culling. I can tell you from experience, they will need to learn from experience, and go through something very ugly before they "get it". Early on we had some issues, and didn't handle them correctly. He saw first hand what I had been telling him, and he finally got it, so now when we need to handle something it's not met with such resistance anymore.
IMO, I think your thought to cull is correct. I firmly believe in having a strong healthy herd, and we have taken on a "cull hard" theory in order to get to that point. It's hard to do, and very sad, but it's just so much easier than fighting illness every step of the way.