There are three beekeepers that I know of who have queenless hives and high varroa counts. I've suggested not requeening until after treating but this is just my thought on the situation.
Beekeeper 1 is Mike Taksdal, (Nonda Zwald's son-in-law). I'm sharing all of this with his permission. He is a very intuitive beekeeper. He believes he lost his queen when he was marking her and heard a little "crack" unfortunately. I will attach the pictures as files so you can enlarge them. The first pic is the mite drop after the first treatment of oxalic acid. The colony was both queenless and broodless. So OA was a good choice. Unfortunately we ordered a queen before we knew the colony had a serious varroa problem. The entire pile in the pic is varroa.
In the second picture, the pile on the left is after the second OA treatment. It was done two days after the first. The pile is a mixture of pollen and varroa but still significant. (The pile on the right is from the first treatment and just varroa, no pollen.) Check out the pics....
So the question became what to do with the caged queen which had just arrived. It would be nice to clean up all or most of the varroa before putting the caged queen in but it's unclear at least to me how long a caged queen stays "good" in a cage. Some commercial beekeepers keep the queens in cages for weeks but that surely is not ideal. I thought/think a week might be okay....
At first Mike and I discussed setting up a mini nuc with just a frame or two of bees. We would tape over the candy end and just let her be "happy" until we moved her to her real home after we got the varroa cleaned up.
Mike came up with the idea of taping over the candy end and putting her in the problem colony BUT removing her overnight on the days he continued to treat with OA. I liked the idea. It was definitely thinking outside the box. So that's what he's doing. He'll OA every three days or so. We'll keep you posted. Please post any ideas or suggestions you have.
The second beekeeper with a queenless, varroa problem has two queenless colonies each with a serious varroa problem as discovered with alcohol washes. These hives had older larva and lots of capped brood. So the colonies were queenless a week or less. Don't ask what happen to the queens. It's basically unknowable...
But because of the brood we put in formic pro which should kill the varroa under the capped cells. There's been a lot of mite drop which is good news. The two weeks of treatment is up this Saturday and we will retest next week. We expect to re-queen later next week. We'll wait until the queens are accepted and laying and then re-test again. If we need to treat, we'll likely use apiguard.
Don't know the story of the person with three out of four hives queenless. I suggested they test before they re-queen. Haven't heard back.
Even if your hives are not queenless, this the time colonies begin to go downhill. It's so much harder to do a hive inspection with two deeps filled with bees and two supers. But it's so important to do that alcohol wash with nurse bees every two to three weeks. In my opinion, if I were not going to test, I would definitely treat with formic pro anyway. It's hard to imagine a colony that DOESN'T have a varroa issue. Yes, it will kill some bees and maybe, even the queen, but doing nothing is not likely to be okay.
Also, I've seen another case of European Foulbrood (EFB) in a hive. Weak colony, spotty brood, uncapped twisted larva, bees dead as they are eating their way out of the cell. It's not my colony, but I probably wouldn't try to save it. Plus since everything is infected with bacteria, I wouldn't reuse the comb and would clean the whole hive with a chlorine solution. Be sure to clean your hive tools between each colony inspection. It would be a shame to spread the bacteria to other hives. I know very little about EFB except, per Caroline Breece, they might get over it if the colony is strong enough. She suggested re-queening but I wonder if that's a wise use of my bee budget. OOPS. I don't have a bee budget but I should!
Wishing you well. Show up for the Hive Dives on Saturday mornings at 10 at the Apiary (but not this Saturday because of the fair).