The speed signal is via the CAN bus from the ABS ECU to the engine ECU, not just the usual pulsed signal. I've not checked but I expect that the HKS speed limiter remover splices into the CAN bus and changes the data so the ECU never sees the speed go over 112mph.
You could try to get the HKS box wired into the CAN signal wires on your HR. Easier (and about the same price I think) to get the ECU reflashed to remove the speed limiter.
EDIT: just checked and the HKS device does splice into the CAN bus. HR CAN bus is on pin 113 and 114. Still might not work as the speed data could be on a different CAN ID, byte or on a different scale.