So good news is that adding a div to contain everything, like you said, got rid of extra paragraphs being added. Bad news, it's still not working...
I'm not adding it at all actually, it's being auto added by my CMS editing program, CM1. Any time I directly copy and paste the JavaScript section of the accordion code in, it just adds CDATA in there. I'm not even sure what it stands for or what it does. When placed in Notepad++ (the editor I use before putting into CM1), I notice that when I test it, the text doesn't come out, which is the same problem I have in CM1. But when I remove CDATA