Yes!
We’ve added new annotations to all rendered widgets to try and make it easier to interact with the widget as a developer. You should find that when rendered a timeline widget (identified with class="twitter-timeline") will have a data-widget-id field (corresponding to the data-widget-id on your original embed code) and a data-user-id for profile widgets, and data-search-query for searches.
We shipped this a few weeks ago and I’ve been meaning to post a message here about some of these new hooks. We’ll get them written up and properly announced in due course. But I’m glad you found it, and yes, these kinds of use cases are exactly what the attribute annotations are for.
Let us know how you get on! Thanks!
Ben