Thanks for the post, Kaleb! I unfortunately don't have any kind of update/new information about a Covenant Eyes iOS extension. It's been brought up a few times in the forum here and each time I have passed the idea to our developers! Having something like that would definitely be a game changer!
As far as a plan to make the Covenant Eyes app more similar to Safari, we do our best to keep the same kind of layout Safari currently has, while also including some of the necessary Covenant Eyes features. Were there any specific layouts/features from Safari that you could think of? I would be happy to share your feedback!