I agree with your conclusion. Since you will be rewriting the web layer and wish to keep development costs low, going the PWA route would be easiest. Another option might be Ionic which abstracts away some of the details of PWAs and hybrid apps into a simple workflow. Going hybrid gives you the ability to use native APIs for authentication, for example, if you would like to get the best of the web and native worlds thanks to the webview.
For the stateless layer, will you be using something like Firebase as the back-end and keeping state in-sync by relying on clientside caching when offline?
