Taras from Langshop support is here. We use 3rd party translation engines for machine translation. As you understand it is never perfect, especially for certain language pairs. We are trying to improve this by changing the algorithm of translation engine selection and including more translation engines.
Also, I'd like to remind that all the translations are editable through the app's interface and exportable, so you can bulk edit or replace translations. Besides, you can send a request for professional translation directly from the app.
Speaking about your Idea of having English as the Base language. It is true that changing the translation direction may improve the machine translation quality. Please note, however, that Langshop doesn't work with Base language. Only with translations. If you change default language of your store, it will not swap translations. It will only mark your original text as created in English instead of Japanese. So you will need to replace the content in the original language yourself. Depending on the amount of content, the process may take a while.
I hope I could shed some light on this situation, Gordon. Type to me or reach our to our Support Team if you have additional questions.