GH is General Hardness (in simple terms). KH is Carbonate Hardness. Your "hardness" level is probably GH so it is kind of low meaning you have soft water. More than likely your KH is very low which is what is possibly causing your cycling stall.
Your alkalinity test (which is primarily made up of KH) results seem to be bouncing all over the place in your established tank and in your fishless cycling tank... but it could be the way the numbers are typed since they did not fall into columns. In the established tank, the test results, if I'm reading them correctly went from 10 to 20 to 40 to 0 and stayed at 0. These seem very inaccurate to me. Look at your log and edit the post if needed. I believe some editing is needed.
On your cycling tank, you show 0 for hardness and alkalinity all the way until the last numbers where they jump up to 25 and 80 respectively. Did you do a partial water change? You are also showing 0 for the pH on the cycling tank and we know that's not accurate or maybe you weren't keeping track. Let me know. Also, you started with an ammonia level of 6 but when the ammonia went down to 1, you were suppose to raise it back to 4-5ppm. Do not go over 4-5ppm as too much ammonia can also stall the cycle. You should have gotten a nitrite reading when the ammonia level dropped. Are you using any kind of water conditioner or dechlor product that advertises that it neutralizes ammonia too? It's best not to use these types of (ammonia locking) products when fishless cycling as many test kits are confused by these products.
For you plain tap water, you are showing 7 as your final number which in your other charts is the ammonia reading. I'm guessing the 7 is suppose to be pH on your plain tap water. Is there no hardness or alkalinity reading on your tap/source water?
Since I am still missing a lot of data, it's hard to come to a conclusion. See if you can answer some or all of my questions. Also, bring the ammonia level back up to 4-5ppm in your fishless cycling tank AFTER you do a 25% PWC (partial water change).... just in case it's a low KH or pH issue so the PWC will add more KH into the tank.