I know one thing about genetics and that is those three won't be passing there DNA genes on

Watch your fingers when doing those two muntys
Instead of always making facetious remarks, why not put your grown-up hat on, and try to have a sensible discussion about genetic improvement in wild deer through phenotypical selection?
I may not know anything much about red deer specifically, but I do know about selecting for genetic improvement in large ruminant animals. It's a subject that interests me a lot, and if, as you claim, you have some knowledge and experience in this field I'd be glad to hear about it.
Unfortunately, phenotypical selection is the only option available to us in wild deer, and it's not particularly reliable as an animal's appearance can be significantly affected by environmental pressures. We also have no control over their breeding, so there is no guarantee that the male that you retained as a "good one" will actually sire any offspring. Selection of the females will generally give better results and a more sustained gain than selection of the males.
I think you claim to have "improved" the quality of your local red deer through your selection process, and I'd be interested to know by what metric you're measuring that improvement? Can you provide the data to substantiate your claim? For example, can you demonstrate that there's been a sustained gain in lean meat yield as a percentage of carcass weight, or that the ratio of high value to low value cuts has improved over time? These are the sort of things that can be measured and recorded, and will clearly show if the selection criteria you're applying are actually resulting in genetic improvement.
The more characteristics you try to alter at the same time, the slower the rate of gain will be, so it's best to pick a few important traits and concentrate on them.
Aside from antlers (which are purely cosmetic), possibly one of the best traits to evaluate in the field in the live animal is body length. An extra 4 inches on the loin of a fallow doe equals an extra £15 income from the loin alone, so selecting for longer animals by culling the shorter ones makes economical sense.
Winter body condition is also another trait worth selecting for, and again it can relatively easily be assessed in the live animal. Need to take care though not to overselect for this and end up with carcasses that are too fat, as they're wasteful to butcher. In an ideal world we would be selecting for loin muscle depth as well as length, but in wild animals we can only assess this once they're dead.
Another worthwhile trait to select for would be early sexual activity. So keep the males that come into rutting condition ahead of their herd mates. This should result in them siring daughters that come into breeding condition early, with a result that, over a period of years, the birthing date of the herd gradually moves forward. This will give a higher survival rate of the offspring through their first winter, and enable you to maintain an economical cull from a reduced breeding herd size.
Selecting for antlers is great if your income comes from trophy stalking, but not if it inadvertently results in you selecting animals that are less suited to their environment. Otherwise, after a brief improvement, antler quality will decline due to environmental pressure. So characteristics such as body condition etc should take priority over antlers.