Instead of removing the fish, take out less water, refill, and start the process over again. It is definitely not as efficient, as you are just diluting the remaining water, but eventually, you will get your nitrates down and the tank clean. It is more time consuming, but you can get the nitrates down to an acceptable level. In the past, I have drained out 1/3 of the tank, refilled, and immediately drained out another 1/3 and refilled. After that, I was out of hot water and had to wait until I had enough hot water to repeat the process one more time.