There actually is a simple solution. The key is to know exactly how the headers work, and how that affects control of 3-pin fans.
Major clue from what ASRock Tech Support told you: both the CPU_FAN and the CHA_FAN1 headers will do automatic detection of the fan type connected, and adjust themselves accordingly. The manual does not tell you this. So that CHA_FAN1 header IS changing itself to operate in Voltage Control Mode, which is what any 3-pin fan needs. However, the CHA_FAN2 header does not do this, it only operates in PWM Mode. And CHA_FAN3 has no control ability at all.
Next we deal with multiple fans on one header. Generally, any mobo fan header can supply up to 1.0 amps for all its fans in total. Now the SP120 High Performance fans's specs say they consume 0.18 amps each, so hypothetically you could afford to connect up to 5 fans (0.90 amps total) to one mobo header. You say you have 3 - or is that 4 with the new one on the way? Do-able.
Next, how to do that? You will be working with the CHA_FAN1 header that uses Voltage Control Mode, and connecting to it only 3-pin fans. So a fan HUB that only operates for 4-pin fan systems is NOT how to do it. You need a SPLITTER. This is a device that looks like a group of wires and connectors. It has one arm with a female (with holes) connector on it that plugs into a mobo fan header. Then it has 2 or 3 output arms each having pins, for plugging your fans into. This device merely connects the fans together in parallel to share the power from the header. It also is rigged (by missing Pin #3 on one or two of it outputs) to send back to the header the speed signal on only ONE of its fans. (To distinguish, a Hub may look like this, too, but it has one EXTRA arm that ends in a connector to plug into a power output from your PSU, and that's where it gets fan power. But a Hub MUST have a PWM signal, and can only control 4-pin fans.) You should be aware that it does not matter whether the Splitter is for 3- or 4-pin fans, because either type will fit your system and connect your 3-pin fans properly.
Here's an example of a Splitter for 3-pin fans with two outputs.
http://www.newegg.com/Product/Product.aspx?Item=N82E16812423168&cm_re=coboc_fan_splitter-_-12-423-168-_-Product
If you buy three of these and "stack" them by plugging two into the outputs of the third one, that will convert one mobo header into four fan outputs, and you could hook four fans up to the CHA_FAN1 header.
Here is a Splitter for 4-pin systems with three outputs
http://www.newegg.com/Product/Product.aspx?Item=N82E16812423162&cm_re=coboc_fan_splitter-_-12-423-162-_-Product
With one of these you could connect three fans to one header.
When you do this, the CHA_FAN1 header will detect that it is dealing with 3-pin fans and start using Voltage Control Mode (as it already has demonstrated it can do), and ALL your case fans can be automatically controlled by that mobo header.