That’s a tricky one, but it shouldn’t be. Last time I played with it, custom roles lacked a lot of “customization”, and I believe it was bugged. Not sure if it has been fixed since then, but even if it had, I don’t believe you could disallow a user to edit their own task assigned to them.
You could however disallow normal users the ability to “Edit” a task, by blocking access to the TaskModificationController. Very similar to below suggestion.