You are on the right track for doing fishless cycling.
We will do our best to help you find the problem.
First we need to go through some basic stuff. Please bear it with me.
1. What test kit are you using?
Paper strip test kits can be very inaccurate. If you are using a paper stripe test kit, we recommend to ditch it. And a liquid test kit is required. The most commonly used one in fish hobby is API Master kit.
2. Ace Hardware could be selling more than just one type of Ammonia. Only one type is (pure).
Are you sure the Ace Hardware ammonia you bought is the correct type?
Please check the label to see the ingredient. Let me know what you see. The type I used had "10% Ammonia Hydroxide, 90% water". Some other types of ammonia product might have soap in there which will kill the bacteria, not only the tank will never be cycled but they also can't be used for fish aquarium at all.
3. Your only have an ammonia concentration of 0.5ppm, and it is on the low side. It is recommended to have it at anywhere between 2~6ppm. During my own fishless cycling, I was aiming at 6ppm ammonia.
4. Have you ever seen a sign of nitrite? And nitrate? Even just a really tiny amount?
5. Have you changed water at all during the last month?
It is not recommended to do any water change until there is high concentration of nitrate.
6. Your PH is on the low side at 6.8. Combined with Prime, my guess is most of your 0.5ppm ammonia is in the form of ammonium. Although ammonium would eventually turn back into ammonia, there might not be enough ammonia for the bacteria to feed on. This is where higher concentration of ammonia would help.
My suggestion would be
a. Get a different type of water conditioner for fishless cycling. One that does not say "detoxify" ammonia, so it will not turn ammonia into ammonium. Something like Tetra AquaSafe. Do a large water change with AquaSafe, anywhere between 50~70% water change should be fine. (This step might not be needed if you do the next step)
b. Raise the ammonia concentration to anywhere between 2~6ppm.
More ammonia available means there will always be sufficient amount of ammonia in the water as bacteria food even if there is Prime in the water to turn some of it into ammonium. Do not exceed 6ppm on ammonia, it can stall the cycle.
For the most efficient fishless cycle with no factor to slow it down, I would suggest AquaSafe over Prime. Prime is a better water conditioner for after the tank is cycled.
As for your question of Akadama, I was unfamiliar with substrate Akadama. A little research had me learned it is just another aquarium substrate and it shouldn't have a problem at all with aquarium nitrogen cycle.
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