Apollo,
The tank is not cycled. The reason you show no ammonia or nitrite (or did when you checked it) is because there is no bio-load to create the noxious gasses. A tank has to be actively cycled and this one clearly is not. Please do not take offense but you asked for some help and we are trying to save the little guy if it is possible so hear me out without being upset.
The rock you used was dead rock so it had no starting bacteria. Simply leaving it in the water does not add bacteria. There are a couple of methods to start a cycle and you need to read up on the processes but you can't do it with an animal in the tank because the purpose is to generate the deadly ammonia that turns to deadly nitrite and starts growing the bacteria that turns that into less impactive nitrate. It is very likely you have both ammonia and nitrite in that tank now from the waste of the prior occupant but the cycle is far from complete.
If the little one responds to the new water, completely replace its tank water. This will NOT cycle the tank and you will need to do daily water changes just to keep up with the pollution. If the larger tank has truly cycled live rock (a picture will be helpful) then you can place some of the rock into the small tank and some of your uncycled rock into the larger tank to start a culture. This does not happen overnight and a 3 month minimum with continually adding bio-load is needed to culture a tank for the waste of an octopus. Unfortunately, anything you try to buy will need to be cycled away from the animals before it can be helpful to the tank (and not doing so will make matters worse). The only reason you can put your dead rock (and then only a piece or two) in the larger tank is because you have had it in the tank for "several months" and it was dead to begin with. If you have friends with an aquarium that will loan you rock that has been in their tank or sump for a long time, this will also help but not cure the current condition.
If you lose the little guy, and wish to maintain the smaller tank read a little on active cycling. The following is a brief description of three of the most common ways to cycle a marine tank but you need to find a full write up to get the results you want.
The oldest method is to add hardy fish and overfeed them but there are better methods today. The object is to create ammonia (the fish eat and eliminate and create the ammonia) that will become nitrite and grow bacteria that will turn the nitrite into nitrate. The nitrate is then removed through your water changes and any macro algae you may decide to put in the tank (not really viable with an octopus) or sump. It is NECESSARY to see a huge ammonia spike followed by a nitrite spike and then smaller ammonia/nitrite spikes as the tank matures. If you never see the ammonia, the tank will not cycle.
One way I have not tried but is written up as working well is to add a dead shrimp (the kind you find in the grocery). How often and how many you will have to find in another forum that specialized in setting up marine tanks but this should give you some key words it it interest you.
Another method, and my preferred way is to use live rock. Finding it is not the easiest and it is expensive. Here again friends can be helpful if they have sump rock they will sell you or if you can find someone breaking down a tank that is still wet. The live rock will have die off that creates ammonia as well as some starter bacteria. After the first month, you would start adding a clean up crew and feeding it. Generally, hermit or other small meat eating crabs are good for the first critters. They will eat meat but also help clean the rock of algae. By the second month you should be able to add larger clean up animals. I find serpent or brittle stars to work very well for this as they love meaty foods, are hardy and can remain in the tank after it is cycled (any crabs may or may not be eaten).