Yes, we have live oaks and a water oak which resembles Live Oaks, however they drop their holly-like leaves now up till about January. They have to be picked up with a mower because of the same situation you have. After the pick-up, I put down sulfur and before the next crop comes down, the simazine a a lower rate. March 1st--almost like clock work the Live Oaks drop their leaves and its all over again. At one time I though about mulching the leaves to help with the acidification of the sandy soil, but that didn't work without mowing too close, so it was back to the pick-up which was sorta nice on lazy days and temps nice.
So in the end--there ain't an easy fix or time on the coast. After that more overdressing with compost around those same trees that zap the nutrients.
We all are merely gleaners from the masters who were here before us.