A site we do a little work on seems to be slipping on some key terms with every penguin update.  Looking in to it they have a lot of exact match anchors on those very terms coming from crap sites.  Looks like the firm that used to do their SEO were pretty lazy in their methods.

No GWMT warning or anything, but it looks like these are not helping the cause.

A stroke of luck though: At some point the URLs changed. Most of the crap links point to URLs that now just 301 to the current pages.   

Thankfully I haven't had to deal with much link cleanup in the past, so I'd appreciate thoughts on this:   If we get any decent links updated to point to the new pages then just 404/410 the old URLs is this likely to have a comparative effect to having the links removed entirely? Or, is there likely to be some residual domain-level signals hanging around.

I just spoke with 2_Much the other day, and she said to try by killing all subpages and building new ones.

the approach sounds sensible.  If you didn't see movement after that, I would disavow the links that you've 404/410-ed

How did it go?  Do you think it cleaned out the links?