Hello; Been thinking about something you posted. That being that cleaning the filter crashed the cycle. I gather you now are reluctant to clean the filter. So let me try to clear this up a bit.
First is that the filter has to be cleaned from time to time. No real way around this. Cleaning a filter can crash a cycle if done in some ways. You already know one of the problem methods.
A way to clean a filter is to have either two filter systems or a single filter system with multiple chambers. This way you can clean one part one week and then clean the other part a week or two later. That way you do not remove too much of the filter material at any one time.
Another thing is to have both types of stuff in filter system. Filters have a main function which is to have some sort of media that can trap solids ( fish poo, uneaten food and such). This filter media is often some sort of floss but can be other material. I call this stuff mechanical filtration and consider it a throw away material. Once it gets clogged with some detritus I throw it away and replace with new mechanical filter stuff.
A practice that has come about in the last few decades is to have power filters do a second job. This second task is to make a place for the sticky film of beneficial bacteria (bb) to form colonies. This second type of filter media is often called bio-media. It is intended to have plenty of surface area for the bio-film of bb to make a sticky film of colonies. The ammonia and nitrite laden water passes over this bb bio-film and the bb convert them into less toxic nitrates.
This filter bio-media should be in a part of the filter chambers behind the first mechanical media. That way it stays much cleaner because the mechanical filter media traps most of the tank junk in the first place. You should not have to clean the bio-media very often, but some care needs to be taken when it does need to be cleaned. If the bio-media gets loaded up with tank crud then it becomes less effective.
I clean bio-media by giving it a light rinse. Say you are doing a water change(WC). You can rinse off the bio-media in the old tank water. The sticky film of bb colonies will not be rinsed off easy. Shake it around to get the crud off. Keep it wet and then put it back into the filter with some new mechanical filter media.
There is more to all this but enough for now. I will close with another attempt to point out that you are keeping a tank that will always be on the edge of disaster because the fish is too much for the water volume. That you are keeping only 40 gallons of water in a 70 gallon tank is making a bad situation even worse. My opinion, based on your posts, is the only way you have a chance is to do large WC (over 50%) very often (say four times a week).