Help with extended cycling problem

Hi all, I've had my current tank setup for the last two years, and a few months ago I got a sudden and drastic ammonia spike. Since then I've been unable to get my tank back to normal levels...

(Long post ahead, I have months worth of data)

My tank is a 10gal (small, yes, I know) for a 3 year old axolotl (Ax, short for Aximili-Esgarrouth-Isthill). I'm running two corner sponge filters, no substrate, a plastic hide, and a handful of small free floating anubias and java ferns.

My tank numbers before water change:
API test ammonia: 1.0
Seachem total ammonia: difficult to read but around 1.0
Seachem free ammonia: 0
Nitrites: 0
Nitrates: 5.0
pH: 6.0 or lower (kit limit)
temp: 23 deg

My tap water numbers:
API test ammonia: 1.0
Nitrites: 0
Nitrates: 0
pH: 7.6 or higher (kit limit)

I've been doing ~40% water changes every 1-2 days, conditioning with Seachem Prime, but every time I test the water before changing it I get the above numbers.

I must have at least SOME bacteria, since my nitrates go up, but my ammonia never goes away. If I try leaving my water for longer before changing it, the ammonia just continues to build up.

I'm currently attempting to isolate the problem by removing everything one at a time. Right now my tank is down to two sponge filters and one confused axolotl.

My other options:
1) Get crushed coral to raise the pH and hope I can keep up with the Seachem Prime to avoid ammonia poisoning
2) Get a new filter (maybe a HOB filter)
3) Get a new tank entirely (I was thinking of upgrading to 20 gal anyways)
4) ??????????

Any advice you all have or any theories about why my tank is full of acid and ammonia would be very much appreciated!

If you're able to upgrade to a 20gal it will be more stable in the long run.
Have you checked your water supply before adding dechlorinator? Mine has up to 1ppm of ammonia. I've found prime does help, but I keep my water changes small where possible so I'm not adding a lot of ammonia.
Are you checking daily for poop/uneaten food?
Do you have a fan or chiller you can use on the tank? You want to get it under 19 degrees.
I use coral chunks in my tropical aquarium as the pH was running at 6 and it's worked really well. I would do some research to make sure it's okay to use with axolotls first.

Thanks for the suggestions! I've had a busy week, but I'm going to buy a 20gal and new filter soon.

My tap water does have ammonia in it, but I don't know if I can do anything about it since the tank water also consistently has ammonia. The weird thing is I haven't fed Ax in about a week, but even with the water changes I still have ammonia and nitrates (my tap water nitrates are 0).

Ax has developed a mild fungal infection today after I neglected to change the water over the past two days. I'm hoping a good water change will clear it up, but if not I'm planning giving him a salt bath tomorrow...

It could be the prime that's throwing off the results. It is a known issue, you can get more info on it on their website. Wait at least a day after adding dechlorinator and test the ammonia again. Do you have any live plants in your tank?

The prime doesn't seem to be affecting my ammonia readings. Ammonia is still holding at 1.0 no matter what I do, but the SeaChem test shows no free ammonia, which is good...

I do have a few small anubias free floating in the tank. They look healthy, but do you think I should remove them?

Other updates: The fungus cleared up immediately with a water change. I installed my new filter, at the moment I'm running both old and new filters. Good news - the pH has increased and is holding steady at a more reasonable number, but now I'm really worried about the ammonia.

I asked about the plants because they're really good with helping a cycle get along. Keep them in, unless they are dying.
What kind of test is the seachem? Is it liquid or strips?

I have both the API and seachem tests. The seachem test uses sensors - it's the one they suggest using with Prime to avoid false readings.

Hm I wonder if it's worth taking a sample to your local fish store and getting them to check in case your test is showing incorrect results.
If you can, tub the axolotl until you can sort the tank out. This way you don't need to do the water changes, maybe it'll help. Do you have any bottled bacteria you can add to the tank?