Wow, Niall! Thanks for the detailed response!
I am already in conversation with United Themes, just waiting for their reply. I will of course link them to this conversation and hopefully they can come up with a fix. The only reason I would prefer to use their bundled Twitter plugin is that it is more in keeping with the design of the theme. However, if they cannot come up with a fix, I will use the generic timeline embed.
Really though, I appreciate the time you took to explain this to me. I can stop driving myself crazy thinking I had created the Twitter app incorrectly!