wet super box they have already started filling
This tells you that a flow is on, in which case they will fill rather than clean combs above the crownboard. Until the nest contracts, the space above the CB has been determined to be within the nest, and bees fill from the top down.
When flows have ceased - drought, seasonal gap, ends of the year - they will clean out everything you give them above a board, as by then the nest perimeter will have reduced below the CB.
to late to let then cap, than feed and treat at the end of the month that feels later or do I just take the partly filled supers off to store?
Treating is a priority and you must decide what you want: bit-of-supers now or a strong and healthy colony in spring. Bees would 'prefer' both, of course, and if we thought like bees (as we ought) that is the port we should steer toward.
In other words, get the supers off now and treat. If the honey is 50% capped and passes the shake test (hold a frame horizontally over the box and shake down abruptly; drops = unripe nectar, no drops = honey) then extract.
Better still, get a refractometer and test each box, even frames. Extract unripe separately and retain it for feeding later, or nadir those combs as Enrico described. Return to the colony nectar above 19% in a feeder; do so at dusk to avoid a feeding or robbing frenzy. Below 19 is good for bottling. Legal limit for honey is 20% but at that point eventual fermentation is likely.
An advantage of extracting the unripe (rather than nadiring) is that the colony will then winter on fewer boxes, which makes life simple for the beekeeper and cosier for the bees, as nest heat will be retained more easily and with less bee effort.
An advantage of nadiring is that bees will have space, should they need it, to expand or store pollen or even nectar in September and October. Don't worry about the bees under the single BB hive: when the heatwave ends they will return indoors, and anyway, it is far better to winter a colony packed into one box than to rattle around in two.
The issue of space for the current flow may be a worry, but what is it that's coming in? Himalayan balsam, which may reduce to a trickle next week?
feed and treat at the end of the month
Feed, yes. Treat? Bit late to clean the winter bees. If using chemical or thymol treatments, then supers off. If vaping with oxalic, you could put a sheet of newspaper under the supers and the OA will affect the BB only; bees will chew the paper away. Repeat 3 times on day 1, 6 and 11.
Wet supers will not go mouldy if stored dry and cold. Honey or nectar in the combs will probably ferment, but bees will clear that in spring without much side-effect. Avoid warm storage and protect combs from wax moth by using sulphur strips or Dipel, and from rodents by sealing the boxes.
