I do see some issues, though not saying these were the actual cause. But combined, may have contributed. I'll explain.
First, I would not use baking soda (sodium bicarbonate). Stanley Weitzman, who probably knows more about characins than anyone alive, has written that this is not a good substance for maintaining a pH balance. He says, sodium bicarbonate has no effective buffer action and cannot stabilize pH in the face of additional acidic waste products. And continual use will cause the sodium ions to reach intolerable levels for fish.
To the nitrates, any level above 20ppm is now believed to be detrimental to most tropical fish long term. Many have written that nitrates up to even 400ppm is not much of an issue, but the scientific data does not support this thinking. I would have to dig into my research to find the specific information, but this should make sense when one realizes that most of the fish we maintain in aquaria occur in water with nitrates so low they usually cannot even be measured. And excess nitrogen in any form, be it ammonia, nitrite, nitrate or nitrogen gas, is detrimental. Even ammonium which is basically harmless is rapidly assimilated by plants. But allowing nitrates to increase to the levels you mention is more than the plants can handle, if they are present.
I would not expect the rapid lowering of nitrates to cause fish deaths, but the elevated levels clearly, in my view, have weakened the fish so this may be one factor in the equation. The pH plays into this; at an acidic pH, ammonia changes to ammonium. But as soon as the pH rises above 7, the ammonium changes back to highly toxic ammonia, and this shock could easily kill some fish. As the pH readings are not absolute, this could be part of the problem. When an aquarium has gone without more significant water changes, it is much safer to change less water and do it more frequently in order to bring the biology back to safe levels.
Which brings me to the water changes. Weekly is the absolute minimum, especially in tanks that are overstocked as you mention. Fish are better able to tolerate gradual changes whether worsening or improving, but a sudden change either way may affect them significantly, even causing death. Not knowing what fish in what sized tank, I can't suggest adequate water changes but assuming there are no plants, half the tank every week is advisable once it is back in balance; getting there i would do more frequent changes with less volume, gradually building up. Even nitrates and pH cannot be used as a method of determining water changes, as some wrongly think. There is all the "crud" that is completely unmeasurable and cannot be removed by any amount of filtration. Only a water change removes this, and it is vital. Plants are the only natural "filters" for this, but that is only workable in very minimally-stocked and thickly planted tanks.
To the other parameters mentioned. Hardness would only change via the source water, unless you have something in the aquarium to affect it such as a calcareous substrate. This is where the water supply enters; if there is any chance that your local supplier might adjust the water chemistry, water changes must take this into account.
Temperature of a couple degrees would not of itself kill fish except perhaps for some highly sensitive species. Many of us do water changes and either deliberately or inadvertently lower the temperature by 3-4 degrees. A similar rise is also in itself not problematic.
Hope this helps in understanding things.