The most recent update (v 2.8, released 11 Dec 2017) has marginally improved this problem.
I still get the error message when opening a document using custom fonts, but the document will now at least open, and the custom fonts are displayed as courier, and are editable.
My custom fonts are shown in the drop-down font menu as "iOS fonts", in contrast to "Office-compatible fonts".
If I manually apply them to any text in a document, the result seems to be something displayed at 0.1 point of text size! I get pages of text that is reduced to small black blob on the page!
It is now possible to make-do, seemingly, but this is still far from satisfactory for a paid service which no longer works as it did previously.