For what it's worth, I seem to have been able to get this working. However, it has required a total re-write of the app, to undertake all the computing in advance, but generating lots of small data files for the app to select based on user input. Almost certainly more efficient computationally/overall, but tedious and error prone. As the data change each week, this will mean processing, generating and uploading 34 files every week. Now seems to work on Starter Plan (may well work on free version, I'll test next month, when I unsubscribe form Starter to see).
My advice, don't upload anything that uses Prophet and/or RStan, and make your app to be efficient from the start.
But, mainly, expect everything to take five times as long as you thought.
Ian