The Phanteks PWM Hub you linked to is exactly what you need.
Two factors to know to begin. First, any common mobo CHA_FAN header can supply to ALL of the fans connected to it up to 1.0 A total current. Secondly, to control 3-pin fans the header MUST be using the older Voltage Control Mode (aka DC Mode), and NOT the new PWM Mode.
The second point above is what limits you. Both of the CHA_FAN 1 and 2 headers on your mobo appear (from the manual) to use only PWM Mode, so neither can control speed of 3-pin fans. And the PWR_FAN header does no control of anything. The Phanteks PWM Hub, which is unique among PWM fan Hubs, does something special. It does not merely distribute the control signals from the host header of the mobo. It actually uses the PWM signal from the header to create internally its own group of six 3-pin fan ports each using the older Voltage Control Mode, which is NECESSARY to control 3-pin fans, and CAN control 4-pin fans also. So, this Hub does two functions: it allows you to power and control several fans from a single mobo header, while avoiding the current limit by drawing all power for its fans from the PSU, not from the mobo header. In this factor it is the same as other Hubs. But secondly it CONVERTS the control Mode from PWM to Voltage Control, thus making use of 3-pin fans possible with it.
Note this deviation from the instructions that come with the Hub. There are many mobos these days that use only 4-pin headers for the case ventilation ports, but do NOT actually use the PWM Mode for control. Like all other fan Hubs, the Phanteks unit REQUIRES the PWM signal from its host port. To prevent the user from having a problem, the instructions advise connecting the Hub's fan cable to the CPU_FAN header, and then plugging the actual CPU fan into the Hub's white Port #1. This is because virtually all mobos either use PWM Mode on the CPU_FAN header, or at least make that an option you can set. OP, you do NOT need to do it this way, because the two CHA_FAN headers on your mobo DO use PWM Mode and thus provide on their Pin #4 the signal the Hub requires. So, plug your CPU chip cooler into the CPU_FAN header. Then plug the fan cable from the Hub into the CHA_FAN1 (or 2) mobo header. Connect the Hub's power input cable to a SATA power output connector from the PSU. Connect all your case fans to the ports of the Hub, ensuring that one of them is plugged into the white Port #1. This is the only port that can return to the CHA_FAN header the speed signal from its fan. If you have no fan on that port, the mobo may send out alarms of fan failure because it does not get a fan speed signal. Note that, like all such devices, the Hub can only send back the speed signal from ONE of its fans, and all others are ignored. So, from time to time, it is your responsibility to check that all the fans are still working, because the mobo cannot monitor all of them for you.
When set up this way, the CPU cooler will be guided by a temperature sensor built into the CPU chip, whereas the case fans all will be controlled based on a different temperature sensor on the mobo.
By the way, those fans MAY have come with optional tiny modules called Low Noise Adapters that can be inserted into the fan's power connection wiring. Do NOT use them when using automatic control. Those modules are for use when the fan is connected directly to a PSU power source with no control possible, and they allow you to slow down the fan. BUT when you are using automatic fan control, they interfere badly with the control system and end up preventing the fans from achieving full speed for max cooling just when your system needs it.