Given the data presented above the entire herd is relying heavily on recruitment to keep its numbers up. What this means is that bucks and does alike are getting wiped out every year in high numbers resulting in very few that survive to reach the older age classes. That is why in all their years of hunting the property, they have not come across a doe that is older than 4.5 years of age or a buck that is older than 3.5 years of age. And as pass-thru advised, most are only 2.5 - 3.5 years of age. In other words, the entire herd is experiencing extremely high mortality.
Although pass-thru did not mention the size of the property he did mention a fairly dense deer population (50 deer/sq mile). What really caught my attention however is that he sees 35-60 deer killed annually along a 3/4 mile section of the road. That's wiping out every deer in a square mile or half the deer in two square miles which, property-wise, is a pretty large chunk of real estate. Pass thru also mentioned that he sees 15-20 yearling bucks each year which means there probably 15-20 yearling does in the area as well. In other words, there's at least 30-40 fawns surviving to be recruited each year. That's pretty high recruitment from the adult herd which is seen regularly from herds that are overexploited (have a high mortality rate). They make up for it by having lots of babies.
So where am I going with this?
What I am finding more and more these days are guys immediately focusing on the bucks and believing there is something wrong if young bucks die. Is this an offshoot of the growing QDM movement? Heck yeah it is. Quality deer management should focus on total herd health not just buck health. Unfortunately the parent program sometimes strays from this philosophy and gets caught up in the buck side of things too. Trust me, I am not trying to single you or any QDM practitioner out. I'm just trying to give everyone advice when approaching a new situation (property). The best thing to do is take a step back, clear your mind of all your past experiences, focus on the property before you, and use the data that is presented to makes sound management decisions. The deer landscape can not only change drastically from county to county but from ridgetop to ridgetop. Remember, each property will always be unique in itself.
Pass-thru-
You're screwed. Sorry pal... :D
No seriously, your best management option sounds like you need to reduce the mortality rate on all the deer in the area and obviously the road sounds like your number one problem. If there is any way to create quality habitat on both sides of the road, specifically food AND cover, to reduce road-crossings out of necessity, I think you'll find many more deer reaching the older age classes. It already sounds as if you are not over-harvesting the bucks, so I wouldn't change you harvest strategies at all. I know, it sounds as if you are in a bind because of the road, and quite frankly, you are. Unfortunately, some properties simply need a lot more hard work put into them at no fault of the property owner. Good luck and I hope you can figure a way to reduce the extra road mortality near your place.
