ok, here is what you need to do. If you already do this than thats great!
Turn of heaters and filters when changing water. Two reasons! 1. obviously it sucks air! 2. When you change water, you are adding chlorine filled water, or chloramine depends on where you live and this kills any good bacteria you may have, which wont be very much.
Use PRIME water conditioner, ( i have tested several brands this is the only one that brought my tap water down below .25 within 10 minutes from a bucket test. if you have high levels in your tap of chloramine, then double your dose of conditioner. The reason Prime is so good is it breaks up the highyl stable compound of chloramine much better that the competitors) have the filters turned off, and vacuum your gravel. Slowly fill the tank back up with water and be sure to add the PRIME first to the aquarium. After you have filled the tank, let it sit for about 10 mnutes or so and be sure to have some bubblers on for oxygen and some circulation. This will give the water enough time to get low enough to turn the filters back on which once you have the tank fully cycled shuld control the remaing chloramine ammonia whatever...
large water changes are the key to getting ammonia down. You need to be doing bigger that 22 gallons. You need to do at least half if not more. Dont worry, a large amount of any beneficial bacteria is not going to be in the water anyhow, it should be in your media, as gravel is only static and is only good once something comes into contact with it.
Speaking of filtration. You say you have HOBs. What kind are you running on a 75 gallon? You need at least 5 times the volume of the tank in terms of flow rate for a canister, and 10 times for HOB. This is for Oscars and other messy cichlids. So your filters should be pushing a minimum of 750 GPH in a 75 gallon tank (75gal x 10 =750 GPH of for canister 75 gal x 5 = 375 gph)
I hope you do not use carbon filtration. Carbon is not needed and bio and mechanical is all you need for a great biological cycle. The more bio media, the more places for good bacteria to grow and control high levels of ammonia and nitrites.
In a HOB what I used to do and still do since I have 2 hobs with 2 canisters on my tank, is to slit the top of the carbon bag, empty carbon out, stuff tightly wil ceramic rings or someother bio media that you get from the LFS. The pad in front of it shuld be facing the water output and this is a fiber/spongelike substance that polishes water and grabs more debris.
Good thing about bio media is it can be rinsed with tank water and put back in, no need to replace the cartidge every month like with carbon!
daily water changes until readings (ammonia and nitrite) are below .25ppm are necessary. Adding bio media is the first thing you need to do or you will have an never ending bacterial bloom.
You have a slow start on nitrates, and it will guarantee to imporve quicker with bio media. your tank is fully cycled but I think your fitration is not sufficient to handle the load. That is why you are having spikes. If this makes sense than good, if not please ask for clarification and I will do my best to help you get through this as ammonia is very toxic.
Are they eating and active??
Need to get this down asap, this harms internal organs..