Although USB mice and keyboards are typically low speed devices, there is no reason that a custom HID device cannot be a full speed device.  That's what HIDmaker FS produces.

On a full speed device, a HID device with only a single USB Interface is capable of up to 64,000 bytes per second per Interface: equivalent to a serial port with a speed of over HALF A MILLION BAUD.

HIDmaker FS easily makes Composite devices having multiple HID Interfaces.  Use these for different functions, or different data channels for more speed.