HOw do I make Google find out that the offending links are gone?
Google may well already know the links are gone, but you may not be seeing any immediate changes because Penguin, like Panda, is being updated periodically.
There may be some AI (artificial intelligence) aspects to Penguin which require accumulation of sufficient data to allow results to be tested and recalibrated. The more data an AI system sees, the more accurate it's likely to be.
Additionally, though, I suspect that Google is checking for things like dodgy 301s (intended to make Google think that the links are gone when in fact they've just been redirected to other pages), etc. This kind of correlation probably takes time. I'm sure there's a prescribed order of steps and evaluations the algo must go through.
I'm guessing, too, that there's a degree of historical data bookkeeping now being factored in that may require a time interval in order to evaluate things like rates of link acquisition. All these necessary delays and interrelated operations, I assume, would prevent results from being continuously updated.
webmaster tools has a submit sitemap area and you can also use fetch as google in webmaster tools this will make google go get your current structure. How ever make sure after you hit the fetch button you do the submit to index and make sure you select crawl all pages.