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Just an idea, if you are part of the same company why don't you redirect the pages from the larger site and point them at your newly designed smaller site? That way you won't get stung for duplicate content. If that's not possible I would rewrite all the content from scratch, the problem with rehashing is that sometimes it's often harder, also you can write optimised SEO copy for your new site to help increase rankings and traffic

If your client is well know in it's industry, it might be a good idea to use his vanity domain since that may be what people are looking for, his name working as a Brand. But I would also buy this other domain you are talking about and create another content more closely related to the term in the domain and related. This way you would have people looking for this specialist + those looking for the products. Just don't put the same thing on both one. Normally when I explain that to a client, they do understand pretty fast that using both the Brand + the product brings a broader volume of targeted traffic then one or another. Off course it his more job in term on Backlinking and Content writing, but sometime you have to take more time to do a better job.

I like the option of doing a no index follow tag. Good call Gianluca. I love reading your advice because it's the result of so much experience!