Having done a bit of a deep dive into modding and turn order now, I'm fairly confident I'm at the level where beating JMK is a dawdle. The main problem comes from LV and JMK being at two extreme ends of a spectrum:
One needs precise strategy and input, with knowledge of how to adapt to any situation (LV's team) and the other is just one of those teams that the AI handles very competently (JMK).
But as I mentioned, I'm at the point where most of my matches are ending with my entire team alive and at full health.