Arturia envision you using the KL61 with their own live performance solution, Analog Lab.
That said, can't you adapt Gig Performer, via some kind of MIDI learn function, to integrate better with your KL61?
I don't routinely perform live but I have on occasion used my KL88 mk1 with MainStage, I can program macros in MainStage to respond to every MIDI event my KL88 is capable of sending: all the sliders, all the controls. Can Gig Performer not do the same? If not, the Arturia MIDI Control Center allows you to manually reconfigure the messages sent out my many of your KL61's controls.