Victory!
Your comment on when we were calling update_field turned out to be right on the money. Interestingly, it was initialized enough to be able to run update_field on regular Text/Number fields, but not enough to allow Repeater fields to be updated.
So, we added an add_action which ensured that our plugin fired after all others had, like so:
add_action('plugins_loaded', 'name_of_function');
This solved the issue! Thank you SO much for all of your help and responsiveness, it is VERY much appreciated! We owe you big time!
