I was wrong about this. Now I don’t know if upgrading the alternator is responsible, but the DRL voltage was ~12.6v on the “low” setting which the Morimoto sees as high enough to toggle the full brightness.
I just bought a 4ohm 75W resistor from Mouser and spliced it in place of the factory resistor pack in the left front fenderwell. This brought the voltage to ~9.0v and the Morimoto does what it’s supposed to.
I will update again if this ends up not working after some time or overheating after more drive time and the summer have passed.