Well...the good news is that the tank is cycling without you even touching it. Bad news is we can't stock the thing if it's spiking up to 8ppm without fish or a (known) ammonia source.
Honestly, I don't have a clue and can't provide an explanation...but I'll tell you what I'd do if that tank was in my house. I'd isolate absolutely everything linked to the tank. Personally I'd throw the filter media in a bucket to keep it wet, tear down the tank, give it a quick sanitizing in a mild bleach solution followed by a thorough rinse, toss the play sand into the trash, go down to the pool store and buy a bag of PFS for $10, set it all back up with the new piece of DW you got, refill it, toss the filter media back in and see what it does. I'm sure the plants are fine to add back in. Unless you've got a jungle of rotting plants I can't see that being related personally.
Just a random experiment so you can rule out the water...fill a bucket with it, maybe throw in an air stone (no real reason there other than to prevent stagnant water), and test the water in the bucket for a while.
Again, it's not an explanation, and this is one of the biggest mysteries I've seen here...but that's personally what I'd do. Replacing the filter media now that you've colonized a ton of bacteria in there would be a crime...but everything else I'd ditch and hit reset.