Unusual question about 301 redirects & SEO

I have an SEO question I'm hoping I can get some help with.

A few years ago, my client re-did his website and moved it to a different shopping cart. Because of this, all of the URL structures are now different, and the person who did the move to the new cart never did any 301 redirects. So he now has over 4,000 broken links in Googles Webmaster Tools.

He also had someone doing SEO that built thousands of links using blog comments, profile links, etc. A ton of bad links and his site got hit from the Google updates. So now it is my job to fix it all.

So my question is this - since most of those blog comment links, profile links, etc link to pages that no longer exist (they just go to a 404 error page), could I just do a 301 redirect for most of those links to a different domain so Google doesn't see those links as going to his main site? There are still some good quality links going to those pages that no longer exist, so I wouldn't do this for all of the links.

My thought is to basically set up a one page mirror of his site that says the page is no longer available, with links back to his product categories. Then all of those low quality links that caused his site to drop in rankings would be 301 redirected to this new page. Would Google still count those as backlinks to his original site, and I would still have to go and get those bad links removed?

Or would Google now count those backlinks as going to the new site I set up?

Just looking for an easier way to do this since most links just lead to a 404 page. Would this work, or do I still need to try getting all of those bad links removed?

Thanks for the help on this - hope I explained this good enough Let me know if clarification is needed.

KT