I agree with SGT. Schultz.
Do you have the ability to measure the temp of your stove or flue?
I think, based on your previous threads, that you aren't burning the stove hot enough and you need to reduce the size of your chimney to not only create a better draft, but keep the entire chimney hot. That means dropping an insulated liner down your existing chimney.
Another thought.... Whoever installed your insert may not have insulated the voids generated between the insert and the fireplace. There may be a fresh air supply cooling off the area around the insert and sending heat up the chimney.
My brother installed an insulated chimney for my sister in the house we were raised in. the flue pipe was upside down.. The crimped ends should be down not up. Many people believe this keeps the creosote running back into the stove . Might go hand in hand as a benefit but in real truth this keeps the draft stronger BECAUSE the outside air has to swirl or change direction in order to blend with the direction of the airflow in the chimney. The little bit of air leakage around a crimp connection can slow / thus cool a draft in a chimney. If the flue to insulated pipe adapter is loose or rusted through (leaking) That can cool /slow your draft. I realize you have an insert but tidbits like this should help you analyze things easier.
An Old Timer saying is you can't build a chimney too tall or too small. Not true if extremes are jacked with but this saying helps you understand a chimney.
Another concept I believe is that a chimney needs to be running at least (internal) 250 F. or more (300 is better) to keep clean. A properly banked stove will burn cleaner but many do not acknowledge the chimney (DRAFT) is still HOT . Your Flame is burning the fuel in the SMOKE not the wood itself.
From what I read in comments above I sincerely believe your draft is 99.999% of your problem. Somehow it is pulling external air allowing the SMOKE (DRAFT) to COOL. The moisture in the creosote is from moisture in the air supply condensing from a cold chimney.
My HUMBLE OPINION.