Well, hey, don't beat yourself up too bad, or give up too easily. You picked a method of hydro that should be the least maintenance, in theory, but in my opinion, only works in certain circumstances. I was pulling for you, which is why the thread got my interest.
If I'm not mistaken, they usually have a soil zone up top, but also grow roots down into the water. This soil zone probably acts as a buffer to help against root rot.
Also, I think people use this method for growing herbs, greens, etc, on windowsills and such. They don't require nearly the light as our plants, so their environment and water aren't nearly as hot as our plants under our lights.
Another reason I was interested in this thread- I don't think I've seen any successfully finish.
It seems like a method of hydro thats just too good to be true, but you might be able to work, if everything is damn near perfect.
I think you would need to be on a cold concrete basement floors, so your water temp stays under 75.
You would probably want to cover the remaining 5 sides of your reservoir with Reflectix, to help keep more heat out of the rez.
A soil buffer zone might help, but if you're in a cool basement, you might get away with bare roots in standing water.
Use LED lights if possible, for less radiant heat in the room.
Add some sort of root zone cleaner, whether live or sterile. Live options include beneficial bacteria, fungi, and enzymes, but should only be used if your temps are low, like under 75f.
Sterile options include hydrogen peroxide, household bleach, or calcium hypochlorite powered pool shock. You can get away with higher temperatures using these, but if temps are high enough, bad stuff can always still take hold.
You could research Passive Plant Killers, or PPKs, if you want a passive hydro system, or so I hear. Haven't personally used them, but I know some people love them.
Any type of hydro where the roots are always submerged, are usually at higher risk for root issues. You could check out some of the simpler active hydro systems, like flood n drain, or even turn the buckets you were using into a recirculating dwc with waterfalls.
Either way, you'd need at least a water pump, and a cycle timer. A couple storage totes, and some tubing, if you're building something new.
Just a few things to think about, if you haven't already.