Remotely manage Gatekeeper
Pretty much any MDM can enable / monitor gatekeeper status.

If you want inexpensive, you can use Server.app for $20 and go up from there. Apple Remote Desktop also lets you automate things. Heck, you could set up ssh keys and use that to run spctl by script.

spctl --status


The manual page shows you how to enable and disable gatekeeper with spctl as well as white list certain apps if you want that level of fine grained control.