Hi Casper,
Indeed this isn't currently possible even with 9.6SP1 at that time. I double checked, but no such requests has been raised in our ER portal (Enhancement Requests), then please file it for a future purpose.
Our other product, Landesk Service Desk is much more versatile for this, but LDMS was meant to be handled by admin people in the beginning and not a larger public.
You may handle this by Enable auditing on the Console on "Edit/Delete/Cancel/Start schedule task", hence you will know who did edit a specific task schedule task (To enable it, go in https://community.landesk.com/support/docs/DOC-29251 and this is the same for 9.6) and instruct these people not to edit of course.
I hope it will help a bit at least!
Good luck!