Is there any way to make a seasoned Linux syadmin productive without giving him full root access?

This question comes from a perspective of protecting intellectual property (IP), which in my case, is entirely code and/or configuration files (i.e. small digital files that are easily copied). Our secret sauce has made us more successful than our smallish size would suggest. Likewise, we are once-bitten, twice shy from a few former unscrupulous employees (not sysadmins) who tried to steal IP. Top management's position is basically, "We trust people, but out of self-interest, cannot afford the risk of giving any one person more access than they absolutely need to do their job."

On the developer side, it's relatively easy to partition workflows and access levels such that people can be productive but only see only what they need to see. Only the top people (actual company owners) have the ability to combine all the ingredients and create the special sauce.

But I haven't been able to come up with a good way to maintain this IP secrecy on the Linux admin side. We make extensive use of GPG for code and sensitive text files... but what's to stop an admin from (for example) su'ing to a user and hopping on their tmux or GNU Screen session and seeing what they're doing?

(We also have Internet access disabled everywhere that could possibly come into contact with sensitive information. But, nothing is perfect, and there could be holes open to clever sysadmins or mistakes on the network admin side. Or even good old USB. There are of course numerous other measures in place, but those are beyond the scope of this question.)

The best I can come up with is basically using personalized accounts with sudo, similar to what is described in Multiple Linux sysadmins working as root. Specifically: no one except the company owners would actually have direct root access. Other admins would have a personalized account and the ability to sudo into root. Furthermore, remote logging would be instituted, and the logs would go to a server only the company owners could access. Seeing logging turned off would set off some kind of alerts.

A clever sysadmin could probably still find some holes in this scheme. And that aside, it's still reactive rather than proactive. The problem with our IP is such that competitors could make use of it very quickly, and cause a lot of damage in very short order.

So still better would be a mechanism that limits what the admin can do. But I recognize that this is a delicate balance (particularly in the light of troubleshooting and fixing production issues that need to be resolved right now).

I can't help but wonder how other organizations with very sensitive data manage this issue? For example, military sysadmins: how do they manage servers and data without being able to see confidential information?

Edit: In the initial posting, I meant to preemptively address the "hiring practices" comments that are starting to surface. One, this is supposed to be a technical question, and hiring practices IMO tend more towards social questions. But, two, I'll say this: I believe we do everything that's reasonable for hiring people: interview with multiple people at the firm; background and reference checks; all employees sign numerous legal documents, including one that says they've read and understood our handbook which details IP concerns in detail. Now, it's out of the scope of this question/site, but if someone can propose "perfect" hiring practices that filter out 100% of the bad actors, I'm all ears. Facts are: (1) I don't believe there is such a perfect hiring process; (2) people change - today's angel could be tomorrow's devil; (3) attempted code theft appears to be somewhat routine in this industry.