@MK3 Is that the only filtration you have, and how often do you take the sponge filter off and clean it? If you can remember, can you describe what the dead fish look like? Are there sores, red spots, missing scales, torn fins? Lift up the gill cover and see what color the gills are?
Personally, I think it's one of those "chicken or the egg" problems where there's not a good answer because there are several things at play. I don't think you were over-stocked for a cycled pond, but I think you were over-stocked for a new pond. It sounds like you don't have an effective bio-filtration system -- those sponges are more for mechanical rather than bio (even though they claim to be), and if you wash the sponge out, you'd have to wash it in a bucket of pond water or treated water in order not to destroy the good bacteria [which you may have done -- but it's still not IMHO very good for bio]. Your pump looks like it's moving a good bit of water which is good for keeping the water aerated. Did you say where you live? And do you know what your water temps have been? Many of us are just coming off some really hot summer temps that have caused lots of problems with our ponds. And smaller ponds don't handle such changes as well as larger ponds do.
Did you say if you'd done a water change (sorry, but I tried going through and there was too much to remember everything I read)? If not, that would be my next suggestion.
______________________________
Not saying this is
the issue, but I do agree, looking at the pictures that the top level of the pond looks even with ground level. Even if there wasn't "run-off" from the yard/patio, water and/or debris could easily come together and mix at some point. As an example, most of us build a berm around the pond that acts as a physical barrier between what's in the pond and what's outside the pond. And again, this may not have a thing to do with your problems, but it could be one in the future. So once we get this all sorted out, you might want to consider a future project to give a raised edge (berm) to your pond. The pond is really lovely, BTW.