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Since then, I've had a look twice, and more than a month on from my first inspection, they're still the same with empty frames and worker eggs, then 3 or 4 frames of brood. On my last inspection, I pulled off the super directly above the brood box, and found that they'd built bridge comb between the brood box and the bottom of the super frames on the same side, and the bridge was full of brood where the comb split (I was going to go onto a brood-and-a-half this year, so left the excluder out). I can't remember where the brood in that super was though but I think it was concentrated on the same side.
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To clarify things in your own mind, the term "Super" should be reserved for 'honey crop super'.
If you are using a shallow as a "half brood box" then it needs to be treated as a brood box - with proper brood spacing of frames (which for me means hoffman spacing and the box having rails not castellations - and especially not castellations giving a frame spacing more appropriate to a honey crop super).
The brace comb is likely as a result of the bees trying to create comb at brood spacing when the frames are too wide. They make double banked comb and all sorts of unhelpfully creative constructions.
You need to keep the brood together - the shallow frames with brood need to be exactly above (or below) the deep frames with brood.
If the bees have created a mess of comb in a (shallow) box with mis-spaced frames, I'd suggest putting it
under the deep box. The bees sorting out process should result (after about a month) in that shallow being empty of brood, with the whole brood nest on the deep frames. Then you can take away the mis-drawn comb.
For a small colony, keeping it as warm as possible is a great help. You can close off any holes in the coverboard, put an empty shallow box above it, and fill the empty box with good insulation material. Celotex-type building insulation board is best, but a bin-bag full of Rockwool (or even packaging polystyrene chippings) will still be pretty good.
A nosema test would be a good idea, but a novice is likely going to require help from your local association (unless you have access to microscopes through your Uni).
... I didn't take anything off the hive last winter: as it was my first winter, I didn't know how much they'd need for themselves, so I thought I'd leave it all and see how much they'd used at the beginning of spring so that I could know roughly how much to leave them next winter. ...
Winter stores.
The rule of thumb is that a colony should have 40lb of 'stores' (honey, possibly plus stored syrup from feeding). That is about 8 'brood' (DN) frames completely full.
Don't leave shallow boxes
above a Queen Excluder - you risk giving the bees the choice between staying with Q and potentially starving, or abandoning Q and moving to the food. (Cold bees, as a winter cluster, can't pop out for something to eat and then return.)
with JBM, they've still got too much space. The rule of thumb with Nationals is to add a super when there are 7 frames of brood.
