You could just dual wire buttons 4 and 5 as well, so that they work via both jamma and the kick harness. There are plenty of options to get around this.
That is indeed not how it works, buttons 4 and 5 are on the jamma harness, and you get button 6 from the connector. Or you can solder/wire the kick harness to the jamma pins for button 4 and 5 (or somewhere else if that is more convenient).
Aha, so this was your top secret plan in the works huh, nice!! Which controllers will you be using exactly? Bonus points if they can be integrated in Home Assistant :D