If you really can trust those employees of yours who've worked with JIRA before to not cause more harm than good, I would suggest creating a new default permissions scheme for your projects. In this permission scheme, you could give the authority you want to a group of users called "Power Users" or "Almost Admins" and then add your trusted employees to those groups. This allows your projects to continue to share workflows if necessary (for example, there are three service desks in my cloud environment that need to share a workflow) while letting your trusted employees edit functionality where they need.
Alternatively, you can create a new project role, give permissions to that role, and then manually add/remove users to/from that role on a per-project basis. Either way, you'll want to have somebody knowledgable (yourself or one of these three part-time JIRA admins) keeping an eye on everything. They'll have less time to work on other things, but you've said yourself that even non-devs are realizing how powerful and important these tools are. These tools are definitely important enough to become at least one admin's first-priority.
A note of caution: it's been my experience that many people who love to tinker don't always see the whole picture nor understand fully what their tinkering does. I've recently had to nuke an employee's permissions because he's proven time and again that even though he can make it sound like he understands something, he doesn't understand the functionality he edits and routinely breaks it causing far more work for me in the end.
A basic understanding of JQL does not make one a sys admin; give power sparingly only to trusted employees or you'll likely regret it.
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