I solved this with the help of this thread.
Counterintuitively, on repeating item containers some input fields work normally, but others you must set your own variables for. I do not know the full pattern and which (or why) some form input fields work in this context and others do not, but no date related field seemed to work.
I had to create a variable and use ‘on input change’ workflows on my date fields to update it. Then when the user clicks the ‘save’ button, the workflow for saving it to the database uses the dates stored in the variable.
I was stuck on this for several days!