If the scene is in a coffee shop, shouldn't you be hearing the coffee shop? I can see the desire to lower the noise of these machines/lights so that they don't detract from the dialog, but taking them out all together might be impossible. The best thing from a production standpoint (moot point I know) is to turn off the machines during the dialog portions so that you have the cleanest dialog, and then adding the sound back in post so you can control how loud it is.
Since it's already shot, and assuming that you can't reshoot, you can try another audio program. Soundtrack Pro is bound to be better than any of the stock FCP filters, and if you aren't getting the results you need with that, you could try SoundSoap, or some other audio manipulation program. Of course, that's more money.
It might be cheaper to kill the audio all together and have the actors record ADR tracks depending on how much you paid them (or if ). Cheaper perhaps, but more difficult and painstaking.
Unfortunately for you, there are rarely any easy answers regarding audio. It's sad how large a segment of filmmakers there is (professionals and non) that treat audio as an afterthought. It was hardly even covered by my professors in college. As an editor I've always maintained that audio is 60% of the final product, more important even than the picture. Because with most films, you could close your eyes and still get the full story, but the same cannot be said of those same films on mute.
Just my 2 cents.
Andy