OP, the overheating you describe in not likely caused by mis-connecting, although possible. It certainly could happen if the pump unit fails, but you think that is not the problem. The thermal paste CAN be a problem in any of three ways:
(a) it may be a poor product, and a replacement with a better paste might help, as suggested above.
(b) application of the paste is important - you must do it as instructed. Too much is just as bad as too little. If the paste is pre-applied to the pump bottom face, usually it has a plastic film over it for protection, and that MUST be removed before installing.
(c) if the fastening of the pump unit over the CPU is not done right so the contact is firm and even, that also reduces heat removal. Check that it is on straight and not loose or wobbly.
Regarding your alternate configuration to run the pump at full speed and let the mobo do all the control by manipulating the radiator fan speeds, that really is almost exactly the same as what the Kraken X62 does. The instructions say to connect the THREE-pin fan cable from the pump to your CPU_FAN header. Any three-pin connection to a header that actually uses PWM Mode for control will leave the fan (or pump, in this case) running full speed all the time. Now, IF the header you use does automatic detection of the fan (or pump) type connected and changes itself to Voltage Control Mode (aka DC Mode), then it will be running the pump at lower speeds when temperatures are low. Or, if you manually SET that header to use DC Mode, the same can happen. But if the header is using PWM Mode (and the instructions do not tell you to set it this way, but maybe should), the pump will stay full speed. The radiator fans' speeds will be changed according to the internal CPU temperature, either by the mobo header if that's where you plug in those fans, or by the NZXT CAM software if you do it as instructed. The differences between these two options is in the fine details of "tuning" of the two different control software systems, but the results should be similar.
So, if you want to follow your plan and skip the CAM software, then proceed as you plan, and I'll suggest how to handle your concern. Connect the pump unit to the AIO PUMP header and ensure it is configured to run full speed all the time, no matter whether you have it set to DC Mode or PWM Mode. Use a SPLITTER to connect both radiator fans to the CPU_FAN header and ensure that header is set to use PWM Mode, because the fans supplied with the Kraken X62, their AER P140, are of the 4-pin design, and that it is set to use the Standard automatic temperature control strategy. You will need a 4-pin SPLITTER with 2 output arms, like this:
https://www.newegg.com/Product/Product.aspx?Item=N82E16812423161&cm_re=coboc_fan_splitter-_-12-423-161-_-Product
Note that this device has only two types of arms. One arm ending in a female connector plugs into the mobo CPU_FAN header. The other two each have male (with pins) connectors to plug you fans into. You may note that of these, one is missing its Pin #3, and that is correct. This fan's speed will never be "seen"; only the fan on the 4-pin output connector can have its speed reported to the mobo. You do NOT need a HUB, which is a different type of device. A Hub has a third type of arm - one that you must plug into a power output connector from the PSU. Although in this case, either a Splitter or a Hub can do the job, the Hub is more expensive and uses up a power connector.