So, after a whole afternoon in the sun, the only thing that drained into the silicone pan was thick sugar water from the cells. What a sticky mess. I was ready to give up, but decided to give it another shot.
This time, I washed the wax first with warm water. This rinsed off most of the sugar water. I also made the thumb-tack holes larger, using a nail instead.
Although it's slow going, I am happy to report that it's working. Beautiful beeswax in the pan: