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I am a bit confused. If old site is radioactive with "large unhealthy backlink history", why would you want to associate your new clean site with that radioactive history?
...since it's likely that your old index page is tainted too, you couldn't selectively 301 untainted pages.
When we are talking over 50,000+ backlinks in Google, it's also very difficult to label which ones you think are bad links. Google doesn't tell you which links are bad, so therefore, making assumptions leaves room for error.
For a resolution, I did receive a recommendation of noindexing the entire site and adding links to related content with rel='nofollow'. Basically, a message tells the customer we have re-branded allowing them the option to go to the corresponding page. Since we can't force the 301s, this seems to make the most sense.
In my gut, I feel that Google wants best efforts made to clean up the old links first, and somehow that's going to override everything else. This is just a gut feeling... no strict logic to it.There's very clear logic behind it: to be able to disavow a link, Google needs to keep at least one or two records in databases: one about the original link and another about it's status. I am assuming they are separate because they are created separately and seem to be parts of separate retrieval system but perhaps they are combined - still they need *some* storage space for the link. Multiply that by the number of datacenters and separate index storages and add whatever other info they chose to store for the link and you get a respectable amount of storage space and therefore power, physical space etc. that Google needs to spend on "remembering" a link that's certifiably bad - even the webmaster on the receiving end of PR said so. Then multiply that by the unimaginable gazillions of such links they already store in their system.