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It is my opinion that no, this wouldn't really benefit you much. You could possibly have duplicate content issues, but you would most certainly have the problem of essentially doubling your SEO work. Having yourselves named after a state is not a huge deal. I worked for a company in a similar situation once and it didn't seem to hurt us much, it's really pretty common. Google provides ways of moving your URL if you wish to do that, but if it were me I'd steer clear of creating an entirely new website, unless you really just want to give your programmer a lot of work to do!

You might possibly setup a new ecommerce site and keep your old one as more of a corporate informational site. You would then want to do 301s (moved content) to the new site from your product pages. I am not fully sure of the ramifications of this (cross domain 301) though, someone else may want to comment on that.

"Write an automated script that monitors a folder on all your clients hard drives"

A don't even think the NSA has come up with something so insidious yet so I don't think thats really going to work

Its become clear the current management in Google hates "SEO". They want everyone to pretend they don't exist and that we're all just back in '95 happily clicking cross site hyperlinks. Fact is, don't get too comfortable with a business or product based around Google SEO, they will put the brakes on once you get to a certain point.