Issue Types Missing from the Default Issue Type Scheme

I have four issue types that are not in the Default Issue Type scheme. My understanding is that when they're created they are automatically added to that scheme. Is there a database tweak or something i can do to add those to that scheme after they've been created? The problem it's causing is that I can't change issues to those four issue types using the "move" feature.

I saw another bug report where the issue type had to be in the default issue type scheme for that to work, and that seems consistent with the results I'm getting.

Workaround:

A workaround has been found. Refer to this article: Issue Types missing, blank or duplicated in Issue Type Schemes

Since the workaround requires database updates, Cloud customers can raise a support ticket to get the workaround applied on the instance.

The Integrity Checker for JIRA should be improved to include a database check for automated inputs that cannot be configured from JIRA's UI.