So, now that I figured out why my YouTube code was being scrubbed, I thought I would create a function to automatically convert YouTube links into YouTube embed code. This uses the new YouTube iframe code, not the old embed code. The plugin is here:
It works with the markdown editor generated code, but I haven't tested it with the wysiwyg generated code. Should be fine. It checks for the url in both questions and answers, with or without <a> tags surrounding them, and replaces them with the iframe content. It doesn't change the database entry, and can be switched off via the control panel. It can be extended to include other video sites, if someone can give me the two variables, i.e. the hyperlink and the code to replace it with.