Do you have an example of where "the ideas don't combine well"? Or where an imperative approach is truly better?

In my experience the solution is often to use the appropriate architecture underneath your UI layer. Basically you build a data structure that represents your UI and always hand this entire structure to the declarative UI layer. Underneath the UI layer, you can still use imperative code to manipulate the data structures. The benefit of the reactive/declarative approach is that you don't have to think about how changes in the data need to be reflected in the UI. That's the framework's job.

Note: With "data structure" I don't mean "build a shadow DOM". I mean something specialized to your use case.