The first thing that I think when I hear fish gasping at the surface is Nitrite. Ammonia can also harm fish gills.
I think if folks are right about too much food starting the problem from what you reported here is what I would expect occurred, But first, an ammonia issue can also be caused by the death of a decent sized fish being missed. As it begins to rot, it creates ammonia. This in turn can cause other fish to die which causes more ammonia. A chain of events occcurs and if not caught, an entire tank can be wiped out.
I have had this happen in one of my pleco breeding tanks. A build up of many spawns combined with a lack of normal maint. caused the tank to crash in much the same fashion as you describe. The result of this sort of thing is the ammonia and then nitrite builds up pretty fast. But, in your case, all the water changes and the removal of the dead fish and the cleaning of the slime worked to solve the problem. By the time you got back home and tested your water, it should have been OK again as your tests indicated.
My episode was worse, however, For one the breeding fish in it cost $1,000 each. Their offspring sold for $100s apiece. I must have removed about 85 dead fish and lost two more overnight, including one breeder. I did massive water changes, removed all dead the bodies and Added PolyFilter to the two Aquaclears on the tank. It also had 4x4x4 in. Poret cubefilter. I was lucky. The remaining breeders made it and they have since spawned a number of times. Also about 15 other fish from recent fry to 3 inch subadults lived. That was purely luck.
If ammonia spikes high enough or nitrite spikes high enough, it can stall a cycle. Water changes dilute the problem until it is fixed.
But, there is one more way I know to cause a rapid mass die off, and that is if something toxic gets into the water. For example, if your daughter had something on her hands and she had them in the water or if there was some form of cleaner or bug spray etc. in the air and it got into the tank, that could do it.
Such a sudden mass die off is not usually due to something that builds up over time as that would cause the weaker or less resistant fish to start to die. Once enough fish have died unseen and were not removed, things accelerate. Ammonia rises and nitrite starts as well and more fish die which just makes the problem worse.
The above is just one set of possibilities but what I suggested is a likely explanation, IMO.
