The cougars don't just eat the deer, they also change the behavior of the deer (as one would if they were constantly worried about killers hiding in the bushes). The only way to restore balance is to bring back the keystone species.
The only thing needed? People shouldn't interfere with nature so much. Let it all balance naturally and optimality by doing: nothing. No research needed, no plans, no guidance, just let the earth do it's thing and Paradise returns quickly.
That's a lot of Lyme disease, deer in your windshield and 10ft tall garden fencing whilst waiting for evolution to turn bobcats into deer eaters. I prefer to turn back the clock and just restore what was removed.
I know. I used to be able to walk right up to the deer when I moved here.
I've chased them off the property enough times though now that as soon as they hear the front door, they run, and they actually go quicker through the yard then they used to.