Just write your core logic in C++, interface it with signals and slots, and you can use the same component with widgets and also with QML.
It is not rocket science, C++ logic allows usage with C++ and QML, JS logic - only QML. C++ and the Qt API is the more sound solution, because from JS you don't really have access to that much functionality of the Qt APIs, only a few methods are "ported" into the QML world. But all the high performance data containers and the execution performance itself is in C++.
If you only need to display results and console is not good enough, I'd rather keep to QtWidgets, because adding the declarative module slows compilation down significantly. The widget module is standalone now, so you are adding "extra" module even with QtWidgets (in Qt4 it was part of QtGui) but it is lighter. After you use widgets for prototyping your core logic, you can then implement a QML interface and just hook that up to the existing signals/slots/properties and bindings using them.
And no, you don't embed QML in C++ classes, it is the other way around, C++ is the more low-level layer, which is used to create QML components. As for the actual instantiation, you can go both ways - if you register a QObject based class to the QML engine, you can instantiate it in QML. Or you could instantiate the class in C++ and only make it available in the QML context - it doesn't really matter. If you need a single object, you better instantiate it in C++ in the main() function and make it available in the QML context, if it is components you intend to instantiate a lot - then create a QML component.
You could prototype the core logic with JS in QML and later port it to C++ if you want too. It looks like twice the effort, but if you make your bed right it is actually a productivity increase, because prototyping is that much faster in QML, catching errors is much safer and informative, and if you make your API well, porting the JS code to C++ is usually a minor nuisance - replace some vars with concrete types, replace some . with -> and stuff like that.
Any "elaborate calculation" you really WANT to ultimately do in C++. Every time the calculation is completed, you can simply emit it as a signal, and automatically display the result to whatever slot the signal is connected, be that in a widget or in QML, or even both at the same time.
