Let's go back to the breathing exercises, remember this is fun!!!
First, my understanding is that you have a 160 DT and 50 gallon aging barrel, correct? Assuming that is so a couple of things
1. Your big water change prior to the fish arriving does not go into the aging barrel first, it can age in the tank. Make sure the temp of the water coming in is close enough to your target that it will be at target when the fish arrive, which depends on how big a heater you have. You can determine your heater efficiency for future reference by setting it about 6 degrees hotter than current and then see how long it takes for the temp to go up 4 degrees. Temp change with the heater fully on is fairly linear no matter what the starting point is up to about 88-90 degrees. I think most folks keep grow out tanks at 84-86.
2. What is your nitrate level now? Also what is your water source?
3 Remember that your system as designed will only drop any unwanted solute in your water by ~ 33% Meaning if your NO3 value was 60 then after a water change it would be ~ 40.
4. Did you treat your aging barrel with a dechlorinator when you added the water. In general, especially if your water source contains chloramines you want to treat within 24 hours of use. Longer than that and stuff can start to grow in tap water and the dechlorinator (if Seachem at least) only detoxes ammonia for 48 hours, after that your tank bacteria has to handle. I believe you indicated your tap was + for ammonia which implies that your water supplier is using chloramine.
5. What would I do with the 50 gallons that has been sitting around for several days? Donate it to the sewer system. Alternatively go ahead and exchange it with 50 gal currently in the DT to drop your NO3 somewhat.
6. Finally with juveniles you may find that you cannot keep your nitrates at your target even changing water daily with only 1/3 your DT volume. Next question is how long should water be aged. Answer is till it is at or near DT temp and pH has stabilized. So warm it and aerate it and track pH and once stable the water is ready for use.