I checked it out with a very knowledgable friend who grew up in very chassidishe circles. He laughed when I asked him why Chassidim don’t say tachanun and said it is simply because they finish too late.
I agree that it was silly of me to suggest shkiah as a limiting point for chassidim, they do indeed hold Rabbeinu Tam for the most part, and were never afraid of shkiah. But Wertheim’s book on chassidic minhagim mentions that many chassidim would daven two hours after shkiah, way past Rabbeinu Tam. Since tachanun after dark is a kabbalistic no-no, it seems that there was never enough daylight to say tachanun.
Also, since tachanun has never been a popular chassidic sport (rebbe’s yahrzeits, etc…), it is not surprising that it was totally disregarded at mincha as time went on.
Closing off, my friend was once caught by his father saying tachanun at mincha, and said to him, “What are you doing? Are you a mishigineh?” I rest my case.
P.S. I have not found this phenomenon of skipping tachanun at mincha mentioned in any official halachah sefer or minhag sefer. I’d be happy if someone found a source or at least an official explanation.