I found that vue does have a way to access the dom directly, via a $refs property on the vue instance.
You can set these in your vue templates, which are comparable to ids but are not in the actual rendered dom. They give you back, inside of vue, a reference to the actual dom element. That can achieve what seems needed here, letting TweenLite do its stuff, and avoiding inconvenience of verbose manual dom navigation or setting a ton of ids.
I'm going to explore that pattern and my question still stands in the general area of good patterns via which these libraries can