str_replace('<br>',' ', tribe_get_start_date()); solves the issue – removing the <br> that caused validation to fail.
You might want to update your examples and documentation for how to access the feed when using mini-calendar and for how to get the feed to work when adding get_start_date and get_end_date. Stripping out the <br> tag ensures validation. Strip_tags doesn’t work because you need a space between the date and the time.