Changing a form value or input field value during the submit handler
Just stumbled upon this and it's pretty dead so here's the answer in case OP still cares... turns out @Mołot is right.

The correct way to programatically change a form's submitted value is actually during validation and not during submission.

If you go back and re-read the documentation for form_set_value(), you'll notice that it explicitly says:


  Changes submitted form values during form validation.