Hello Adam,
I am really sorry for the delay of this reply as it is a weekend for us here. There seems to be some misunderstanding here. Let me just try to simplify this a little:
1. When you are writing your blog post with your favorite WYSIWYG editor, there are "html" codes being generated.
2. When you publish your blog post, these html codes will then be displayed on the front end when people visits your blog post.
3. Because of your Joomla template, it's overriding these html styling or typography if you call it. Hence, you don't really get exactly what you are seeing when you are writing your blog post because those typography styling are kicking in to reset the styles of the text on the front end.
Does this make sense to you? Anyway I can really easily provide a quick fix if you can just provide me some sample URLs to the blog post but I would personally prefer that you start a new thread instead.