Doing big water changes will not hurt your beneficial bacteria because the amount living freely in the water is very small.
How high is the nitrite? If it's over 0.5 parts per million, it is quite toxic to fish. You can use prime water conditioner to emergently bind the nitrite while doing frequent water changes to make the nitrite less toxic.
I would do a series of 50% water changes every few hours until the nitrite is 0.5 or below, and dose Prime accordingly.
The Nitrite portion of the cycle was the longest for me when i cycled my 55 gallon. It took almost 6 weeks for my bacteria to catch up with it. During that time, I was doing daily water changes, and dosing with prime. I was lucky, and didn't lose a single fish.
Keep up with the water changes and your fish should be ok.