I'm 100% behind you on this one. I did my cavern in singles a while back, but when I did intro I had already converted over and was diving exclusively doubles. There was no chance in hell I was going to dive singles for the class... or any cave diving after that point.
The rule, IMHO, is pretty friggin dumb. It's a lot like the 'no gloves in <wherever>' rule to prevent the people from touching the coral. It's one of those rules that is meant to protect the stupid by adding risk to those that know *** they are doing.
I never had any trouble at any site during my period as an intro diver with my doubles. I imagine the only way you have an issue is by renting the tanks from them, so they know your cert vs. your equipment.
I'd say just rent the tanks from CE or EE, and just go in and get your ginnie "Intro" wristband and be done with it.