The polyester yarn is pulling much too fast. An hour or two before the reservoir overflows. If the water level in the bottle is more than two inches below the lip of the bottle it doesn't pull at all. I need to try a different material.
What kind of difference does the pickle jar make?
The more surface area you have, the more water is going to evaporate, creating higher humidity. A shoelace maybe half as thick might be better. Also, keep track of when the humidity spikes. At night? Right before a storm? When the water level is higher in the jar?
Consider a test where the lace...
Any kind of string can work. Put 4 or 5 strings of the right thickness but different materials in a glass of water. Whatever you have. Wet them lightly and see how long it takes for the water to drip into a dish under the other end of the string. For some it can take hours, for others only...
Consider a different type of string. Natural works better. Just like a lamp wick, some types will suck up the water more easily. If your "wick" is dry, it's not drawing well enough. Also, wet down your shoestring well before you start the process or it may not have enough power to get the water...