What have you been doing to assess for mites, not just trying to observe them? Without (at least) sugar rolls you are flying blind at this time of year.
You also haven't described the state of uncapped larvae in the colony - what do they look like? When people are suggesting EFB or PMS based on your mention of the shot-gun brood pattern, they are keying off what is an end-stage symptom of things that are better sorted out based on earlier signs.
PMS, of course is a long-running, or overwhelming, state of having an excess of varroa. Regular mite board counts (every week) and/or monthly sugar rolls give the needed info for that diagnosis.
I do sticky board counts on every colony, every week all year long (even in my cold NY winter), and I do sugar rolls on every colony once a month from April to late Oct. I always have a very good idea of what my mite status is, because I hate mite-y surprises. This also allowed me to stop lurching from crisis to crisis of mite levels and make a plan to deal with them on a year-round schedule. And that (along with constant monitoring to verify my plan is still working) means I can treat a whole lot less frequently than most people need to do, with better results.
In EFB, unless it has reached really critical stages, you will see ample evidence of eggs and very young larvae, but few of the larvae are pearly white, fat, cell-filling late stage larvae or pre-pupae. EFB affects larvae 4-5 days old and causes them to twist, slump, yellow, turn grey-ish in their cells, and die well before they get to the capping stage. Though you can expect a few that were infected late in their development to get capped, which results in perforated cappings when the bees pull the dead ones out. Hives can struggle on with EFB when enough larvae escape getting sick to make replacement bees. The shotgun brood pattern occurs when the larvae die before capping and as a result the cell is not capped like the rest of near-by ones.
Queen problems can also manifest as a shot-gun pattern, so the first step is to locate areas of eggs and note whether they are in swathes where every open cell has a roughly same-age egg. That means that at she's least laying well, and that she has enough eggs and sperm for the job. Sometimes, though, queens can be too in-bred and some, or a large part, of the resulting pupae will end up being turfed out by the worker bees who can tell if that is a problem. This creates a shotgun pattern in the patches of brood. She may also not have been well-mated and could have run out of sperm, so all her babies will be drones, often laid in worker-sized cells which make for an unusually lumpy brood capping pattern. (Lumpier, and more, scattered, than typical whole patches of drone laid in drone sized cells.) Bees will often supercede a queen that turns into a drone-layer, which is what happens when she runs out sperm. They have to catch it early enough so that she still is laying at least some fertile eggs, however, for a supercedure to be successful.
So, my advice would be to immediately do sugar rolls on both hives (even thriving ones can have huge quantities of mites at this time of year, particularly in their second summer.) This will help the differential diagnosis of the problems on the weak hive. It would be best to have had done sugar rolls all season so you could have improved information to use now, but better late than never. I use - and teach -Meghan Milbrath's Michigan Method of Mite Monitoring, which I saw demonstrated as performing as well as alcohol washes last summer at the NYBeeWellness Conference, and not lethal to the tested bees. You can find info on it by Googling: "Michigan Mite monitoring" It's easy to learn, though sounds complicated at first. Doing them often and regularly in the warm months will build your skills, so it will become just a routine maintenance chore when doing inspections.
EFB is dxed by looking for the signs I described above,. You can buy good, one-use diagnostic kits for about $12-13 each from some bee suppliers. (I got mine from Betterbee.) And you can also, once again, send a piece of the affected comb to Beltsville for a free examination, but sometimes that takes too much time to get the results, especially at this time of year in a cold climate. If confirmed, you may be able to get a prescription for antibiotics to treat it.
Queen issues are more subtle, but it starts by really studying her work product, which is your brood, from egg-stage to capped stage. The frames will tell the tale, if you can decipher them. This is something that takes ongoing observation, probably for many years, to really master. But the basics are do-able even for beginners: eggs? solid pattern? mixed age larvae? solid pattern? late-stage, fat white larvae and pre-pupae? large patches of capped brood with slightly domed caps? mid-aged capped brood with no holes in them? later-stage capped larvae with some live bees emerging?
I didn't see any of my queens until the spring of my second year. I nearly dropped the first frame when I finally saw one! She was nowhere near what I had been looking for, or expecting to see, even though she was a nice fat, solid brown-bodied queen in sea of smaller, striped girls. Looking back I can't imagine how I missed her for so long, but I did. Once I found one, then I quickly was able to locate the others even though they didn't look at all like the first one. Now I recommend marked queens for all novice beekeepers, even though it delays development of "queen-eyes" when you have the "cheat" of a brightly-colored dot to go by. I also mark all my own, too, since it's handy to know that the same gal is still there from inspection to inspection and year to year.
So seeing your unmarked queen may not be a big deal, but seeing constant evidence of her work, is absolutely necessary. And anybody can learn to do that, just by keeping track of what you see from one inspection to the next.
There is a handy writing surface on the top of each frame to make notes of where you saw eggs/larvae. capped brood on the previous visit. It really helps a lot to watch the same area go through the stages of development. I use a paint marker pen for that on my plastic Piercos. If you have wooden frames, a Sharpie works just fine.
If you can use a microscope to check for tracheal mites, then upping your observational skills to study your brood development patterns and find your queen should be duck soup.
BTW, if you find too many mites and decide to treat, MAQS, (formic acid) is usable with the supers on, and will also kill tracheal mites as well as varroa. I deliberately switch up to it every once in awhile (from my mainstay, oxalic acid) just for that purpose. Formic acid is a treatment allowed under the Certified Naturally Grown Label, which is what passes for "organic" certification in the case of honey. It's chief drawback is danger at higher temps, which may not be an issue for you in ID. I would not use it much later in the season than now without a known source for a mated queen should something happen.
Hope this helps you figure out what to do. I also second (third? fourth?) the advice not to move any frames from the sick colony, or combine until you've figured out what's going there.
Nancy
