A diapause, hibernation in winter ONLY occurs to those emerged in time when it is not a beginning of spring-summer. Any specimens emerged at the right time DOES NOT require to hibernate. NOT A NECESSARY STEP to go through. I know, Vegas is getting pretty hot right now... It's rather difficult to keep the temperature low even with a decent AC. If you want to keep him in a diapause, Only thing I can recommend you is to get a small fridge that you can control the temperature by "numbers," not "low to high." Which is usual way of controlling for wine coolers. If that is out of budget, there is always an option to choose: install a controller on a regular fridge! Not a difficult thing. Ten to twenty minutes research should do enough to understand a concept. I made couple of them when I reared birds (not a fridge, but an incubator). The good temperature for lucanids to go diapause and go through hibernation, may different per species, but in case of L. elaphus, it will be somewhere between 64-68˚F.
I never heard of anything like "fewer deposits of eggs." because MANY beetles in a person's care rarely ever go through hibernation. I have no clue where Alex Shaffer got those information, but I highly doubt that is true. Also, how can you POSSIBLY compare? When a specimen goes through a hibernation, it can't go back to the time when it didn't go through the hibernation to compare. The hibernation has nothing to do with their behaviors. Hibernation is only occurs to those emerged in late summer. Since it is too late to find food sources or mates to reproduce and to survive as in species-wise. When beetles are kept by a person you can actually get MORE EGGS than when the beetles reproduce in forest. Because you will feed fresh food daily, plentiful substrate and space to lay eggs, and if you take a female into another set up every now and then, a female WILL more and more eggs. I don't know how often you pick up eggs and how many eggs you have ever got from your beetles, but you can get around 90-100 eggs from stags, and about or over 100 eggs from scarabs, if you take a good care of them, and pick up eggs weekly-biweekly.