Without a proper vetting program for damage hunts it's impossible to know who will show up. If you only have elk on your property 10-15 times a season, you want to make the most impact on that herd as you possibly can when elk are present. It only takes a few duds and serious wounding events to turn landowners off to damage hunts. Often times landowners participating in a herd reduction program have adjacent landowners without the same goals in mind, thus why the herd got out of control to begin with. Most working ranches don't have unfettered access to these problem elk, but they often come through like a bull in a China shop from time to time in massive numbers.
If there was a way to vet hunters that can sign up for the damage hunts, that would be better. Same as limiting the hunter to being local to the property (faster response time when elk are present) and have a list of their avalibilities to hunt (so you're not making 47179 phone calls to turn up 2-3 avalible and competent hunters)
It's a shame when you only get a crack at the problem herd every couple of weeks and you have someone that is incompetent show up to simply come out and bump the herd off. Just to have them come back in the same numbers and cause mass amounts of damage at a later date.
When it comes to connecting hunters with landowners I really do believe a state liaison position would be beneficial as well as vetting the hunt roster in a way to know you're getting competent and avalible hunters. Some landowners could even add stipulations that hunters have two valid elk tags in their pockets to make sure you maximize the harvest when herds are avalible and grossly over objective.
I don't believe we need more tags per hunter, but rather an improvement of our current systems and processes to make them more efficient and less stressful for those involved.
Let the people shooting their unsighted 30-30 at 400 yards participate in public land hunts and save the management hunts for those that take it seriously and can have a real impact on the management of our herds. Remember that keeping herds within objective in some units can be beneficial to the resource overall, that's what we all want or should want in the long run, while still maintaining opportunity for the general public (granted they put some work in on their end).