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Unfortunately, I don't think there's any easy/fast way to do this. I just ran a test to see how long it take Google to actually obey a noindex tag, and it's taken a little over 2 months for them all to be removed. I had 2 WP blogs that I added the noindex tag to all category, tag, and author pages and monitored the index count 4 or 5 times per week by running site:example.com inurl:/category/ queries. There was a lot of fluctuation at the beginnning, but eventually took hold after about 2 months. On one of the sites, I did add an XML sitemap with only the noindexed URLs on it, submitted it via Search Console, but that didn't seem to have an impact on how quickly they were dropped out. See the screenshot below of my plotting of indexed pages per subfolder: jHm7CkD

"_Could it be dupe content from the W_ikipedia pages we imported and indexed?" That's not a good idea. I'd either point to the Wikipedia pages themselves, noindex or canonical them (back to their source). Also, agree with Clayton John. It could be any number and/or combination of factors. Glenn Gabe, president of G-Squared Interactive, watches website traffic trends and fluctuations and comments upon possible root causes. He remarked back in November that "The fall of 2016 has been one of the most volatile ones I have seen in a long time algorithm update-wise" and observed that Google is testing its new mobile-first ranking algorithm. Check out that article to get some other suggestions as to possible root causes.