What could be causing this leaky evaporator problem?
The condensate collection works by allowing the water to run down along the fins and collect in pans on either side of the 'A'. Upflow systems work a bit better because the air flow supplements the water's tendency to adhere to the fins, whereas downflow systems tend to encourage release. Typically, even downflow systems collect most of the condensate. One problem that can occur is dirt collects on the fins, causing the water's surface tension to break. Surface tension is what causes the water to run down along the fins instead of straight down.

Another problem, which is probably what you are seeing here, though the others may be contributory factors, is simply just too much humidity. With high humidity, so much water develops of the fins that there is too much mass to be supported by surface tension and the water simply drops straight down instead of running along the fins.

So part of the solution may be to mitigate the contributing factors. If you can cool with a lower air flow, that will help. Change filters frequently, which it sounds like you are doing. Reduce the humidity in the house. This is easier said than done. But short of installing whole house dehumidifiers, be conscious of lifestyle habits that generate moisture and try to minimize it, such as always using exhaust fans when showering and cooking. Clean surfaces with liquids during the cooler parts of the day. Try not to breathe too much :)

I don't think you will fully mitigate the dripping with such measures. Moisture happens, and it will end up on the ductwork. You should consider fashioning the portion of the duct on which the water falls into a wide shallow funnel to collect stray condensate droplets and pipe it off somewhere where it can be safely removed.