[support] D7 Adding content to an empty region from template.php

I was asking a slightly different question in the themes list, but I've narrowed down my issue, and believe it's more of a support question than a theme development question.

I am trying to add content to a region from within template.php. The region has no content prior to doing this.

I have tried drupal_add_region_content() from template_preprocess_page, template_preprocess_html and template_preprocess_region.

I've also tried just making an assignment to $vars[page][my_region][my_section_name][content][#markup] from the same functions.

Nothing results in output. Do I have to do it using hook_page_build from a module?