I tried to respond a few times but stopped because it got too long.
It's a complicated question, sadly above our pay grade.
Deep State is today, largely a Republican messaging tool, it's both an excuse and a pinata rolled into one. As phony as most such messages.
Democrats from what I can tell are not blaming "Deep State" in the same way/frequency (if at all?). Barr is not deep state, he's a Republican who served under Republicans who was picked because his view on obstruction was that obstruction by way of exercising presidential power, is impossible. That's shallow partisan, not deep state.
As to your better overall question, how do we get to a more just/reasonable government...well, that's the question the founding fathers tried to answer based on deep philosophical reading and thinking a long time ago. So long ago, that our understanding of things has progressed well beyond the early days of the Republic, but change is not so easy to come by once established, and once powers get entrenched.
I suspect one could look around the world at governments that came later, sort of using lessons learned from the U.S. case, and who might have some better aspects of government. I have no doubt a lot of our political woes are a result of a poorly designed system.
On the other hand, to some degree, entrenched powers will *always* seek loopholes and engage in corruption, so that maybe no system is foolproof, because if they have power, they can use that power to get more power.
Somewhat less seriously, I think its beyond our ability to perfect and administer, as flawed humans. We can envision it, and maybe get a good plan enacted momentarily, but it will always be corrupted.
AI is the only way to do it in a near ideal manner, IMO. Laws can better be described in some systematic/logical fashion, that better models loopholes, balance of power, corruption resistance, etc., we just have to get there. I don't really think we will get there in th next 40 years. Maybe not even 100.