Condensation question?

[dmlefevre]

Hi - I have a 2 flue chimney with a fireplace on one side and a wood stove hookup on the other. Woodstove runs 24/7. Both flues are covered with a cap – 6” screening with stainless cover. Very seasoned wood. Recently I have noticed condensation on the flue cap cover that is dripping down the flue into the cleanout and weeping out the base of the chimney (messy). Had the chimney guy out the other day and no breaks were detected. Cleanout door is insulated to prevent air leakage (chimney guy liked that). Was told to remove the cap cover and see what happens. Well, it is now dry, no more weeping, but I would like to cover the flue again. Thoughts? Can I extend the screening below the cover from 6” to 12”?