I guess it all depends on the relative importance of the keywords and landing pages. If the pages that were hit are important landing pages that drive conversions it should be something that is addressed. If the pages are being penalized, on-page optimization probably won't help too much; however, building quality back links could have some benefit.
It's possible that rankings have decreased on certain pages because the links that were helping the pages rank are no longer valued, rather than the pages receiving direct ranking penalties. If this is the case than building some quality links to replace the ones that are no longer valued may help the pages rank well again.
What worries me the most is when you say the company is going to switch to "white hat only for a few months" (not exactly sure how you meant it, so forgive me if I read into it wrong). Things are never going to improve if white hat tactics are only a temporary strategy. Google is only going to get better at picking up shady tactics.