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Its better to adopt a proactive approach instead of sitting back and wait for penalization. If it makes you feel unnatural then it is the case with Google spiders as well. Later or sooner if there system picked your site for scrutiny they can creates problem for your website so its better to cleanup such links and as a last resort you may use disavow tool. Always record your communications whenever you have such problem you can show that to Google webspam team as a proof of your sincere efforts. I hope it helps. Thanks

Ditching your domain is a little drastic. The question is really how bad are these links linking to you. You don't have you answer this but did you buy links at some point? If you did, start by checking those. "I'm going down the route of initially trying to manually remove links and then follow on with disavow." - that's the right path. Keep at it and submit yourself for reconsideration requests if you received anything in Webmaster Tools. To get back on the path to growth try checking into Broken Link Building. It's an easy way to get a few links and considered a White Hat technique. You'll be able to increase your links a bit here to help boost your organic growth and get back on track.

The thing is the site is not losing traffic, else I would agree. Historically the homepage has never ranked well for the main chosen keyword - highest I think is page 2 or 3 previous to migration to Magento when it started to drift.  Overall organic traffic to the site has steadily risen since the beginning of 2011 and the homepage is ranking well for some longtail variations of the keyword.

I'm going to take the easy way out and side-step the topic of PageRank, which Alan covers well, and raise the issue of relevance and weighting based on reasonable surfer assumptions. Generally speaking, the first link on a page passes the most relevance, and links from unique domains pass more equity than links from previously linking sites. Meaning each new link from the same domain doesn't pass as much equity as the first link from that domain. It's the law of diminishing returns. http://moz.com/blog/10-illustrations-on-search-engines-valuation-of-links From a practical point of view, I try to get the highest link on a page. After that, I don't worry too much about additional links to the same domain on that page. But there are a lot of factors that play into this, and your situation may differ.