Malek you did some good research here. My perspective comes from having a boat livewell. That is much different than your situation because I am able to recirculate fresh water which makes it a lot easier to keep bait alive.
For the conditions you are fishing you seem to be very thorough in your investigations so I would suggest you research urea content of various baitfish and try to experiment to see which species produce more. Also which species are hardier.
For instance you use bullheads maybe they don't excrete a lot of waste. Small bait like killies seem to excrete a lot of urea so that is why you want a continuous flow of fresh water or keep them out of the water on ice. Since your system uses the same water I would think the urea content would be important. You could also think about changing out that water 5 gallons at a time. Only you would know which bait fish are more hardy and which ones aren't. The urea content should be a deciding factor in how many fish you can keep in the cooler at one time.