Since I'm fairly new to chicken raising, I've been experimenting with supplementary light this fall. My hens stopped laying in late September. It took several weeks but they started picking up again when I added a light on a timer in the morning. Like yours, mine comes on at 3:30 and goes off at 8:30 in the morning. This helped a lot and their laying began to pick up. But when I also added an hour of light at dusk, their production doubled within about four days. This is totally unscientific, I don't know if it was the added light or just a coincidence, but I'm pretty happy with the results.
My coop has two windows one each on the east and west sides, but on overcast days the coop is still too dark. I leave the light on all day when it's cloudy outside.