How to add a block to a region in html.tpl? I'm using Drupal 7.

I have a custom template html--custom.tpl.php.

I have a custom block that contains the main menu. This block is enabled in the header region of block admin.

Up to this point, everything but the menu block prints.

How can I print the custom block in the header region of the html.tpl file?
You should make a new theme region similarly to how the header section works and add your block through the block admin into your new region. Rather than trying to get a block to come out in any other way

See this for more: https://www.drupal.org/docs/7/theming/assigning-content-to-regions