Okay. So I shall leave the previous theory I had embraced in the dust...
Moving beyond that, here are some other factors I have been thinking about before I move on to a water change on both tanks today:
1. What about gravel vacuuming during this time? Along with the water changes, should I be doing the standard gravel vacuuming as well to release uneaten food and waste, or should this be allowed to remain so that bacteria begins to populate the substrate?
Vac 1/2 one week then the other 1/2 the following week. You dont need to go crazy but allowing tons of waste & debris to remain in gravel will lead to future issues as you are already aware. Bacteria excrete a sticky substance that allows them to adhere & colonize on surfaces so you will not be removing them.
2. What about filter media at this point -- should the cartridges in the Aqueon HOB be rinsed in removed tank water, or should the sponge in the AquaClear be squeezed and rinsed out in the tank water? Or should these pieces of media be totally left alone right now to colonize bacteria? Neither the dual cartridges of the Aqueon, nor the white sponge block of the AquaClear, appear overtly filthy or blackened with debris right now; on the last water change I performed, last Monday, I dunked the Aqueon cartridges in removed tank water because they were a little discolored, but this didn't seem to remove any attached debris to be honest. I haven't yet touched the AquaClear's BioMax rings or the sponge...
Leave them alone until the tank is fully cycled UNLESS they are so full of debris that water can not flow through them. They should be discolored.
3. Exactly how much water should be removed from the 60-gallon right now if I am going to attempt a change? The reading yesterday, once again, came back as being
no higher than "0.25ppm" for ammonia with 0ppm on nitrate and nitrite, so how much do you recommend I change today?