Hive check

Opened the hive today. About a week ago, I stopped offering the sugar syrup because one refill (about a quart) lasted the girls more than 4 days. I figure that means they've found nectar flow somewhere. In the Sanctuary, plants seem to bloom a bit later than they might in full sun or a little further south. So in the bee grotto, our devil's walking stick isn't flowering yet, but driving around the region I see plenty of it.
At the back of the hive, behind the follower board, the floor is littered with varroa corpses. I saw bees moving them around, and I didn't see any at all on a bee, nor did I see any workers with damaged wings. In the hive proper, at the back where there are unfinished honeycombs, I found several hive beetles, most of them under savage attack by a bee. I dislodged and/or crushed 5 or 6.
The bees are beginning to fill those rear combs, but I wouldn't say we have a surplus, just yet.
In the brood area, I found: no beetles; plenty of fat larvae, and far fewer varroa specks on the floor. The bees in general were very active, responsive, and curious about me.
By the way, I am still working without a veil, and have abandoned our improvised smoker, as well as the long sleeve shirt and long pants. I have been wiping Beat It over my face and shoulders, at first just because the mosquitoes are really fierce this year, but I think it influences the bees too. Guard bees certainly check me out, even hang out on my hands, but they don't get aggressive.
There were far fewer other pests like cockroaches, spiders and ants--in fact I didn't see any at all. I attribute this to the shims Mark cut for me, to replace the bamboo sticks I was using to space the honeycomb bars. The new shims are a much snugger fit and I don't think as many pests can squeeze in. Also, of course, the bees are clearly feeling much better and are doing a better job of defense.
One of the women who got a hive the same time we did reported that her family harvested about 2 quarts of honey from two combs a few weeks ago, so apparently not all the hives ran into that dwindling problem. Her hive is also in town where there are many more ornamental plants providing nectar.
I have an idea that I'm not sure how to execute. In our house, to control roaches, we use common sense techniques like keeping the kitchen clean(ish) and I strew diatomaceous earth around baseboards and under the stove. If things get out of hand I buy those little roach motels. They contain bait, and a poison, and are sized for the bug you want to trap. Pets and everyone else are not exposed to the toxins. I can't help but imagine a SHB sized trap with DE or some other mechanical bug killer inside. The opening would have to be too small for a bee, but the beetles could be baited in with honey and trapped.
At any rate I plan to construct our next hive with a mesh bottom, so those varroa corpses and SHBs will fall through to their deaths onto the DE treated ground below.

In most of the natural world, infection, predators, and parasites are most attracted to vulnerable organisms: the old, the starving, the weak, the already ill. A healthy creature, whether it's a well-nourished human, tomato plant, or bee will have worthy defenses to keep attackers in check. So our goal as beekeepers must be to keep our bees healthy and strong, and not dependent on chemical crutches.
As I battle to rebuild my own immune system, damaged by pollution perhaps, or over-medication, or genetic weakness--it seems to me the bees of the world are on the same path. And although chemicals--medicines--may keep an individual alive, they are no path to a stronger species.