What's holding me back is my fear of losing all the SEO traffic my posts at site.com/blog/post have already acquired.
Would implementing this fix negatively affect the page rankings of my posts and if so, by how much?
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Well you are changing URLs which WILL impact your SEO. The best way to minimize this is with what's known as a "301 redirect".
The 301 part is a server response code to tell the visitor (Googlebot is the one you care about) that the resource formerly at domain.com/page is now permanently moved to domain.com/blog/page.
If done properly you can modify your URL structure w/o taking a rankings hit.
Here is the format for your situation. Paste these in your .htaccess file after the Wordpress section:
# Old URL redirects redirect 301 /oldpage/ http://www.domain/new/page redirect 301 /oldpage2/ http://www.domain/new/page2
You will create a new redirect line for each URL that is changing. Over time, Google will pickup on the 301 code and update their index with your new URLs, assigning the page rank from the old URL to the new page.
---- EDIT ----
To run Wordpress in a sub-directory without including that path in your URL structure, you probably want something like this article Giving Wordpress its Own Directory