I would steer clear of removing 250 blog posts from the other web properties. They may be driving traffic to those websites.
The client is requesting 250 particular blog posts to be rewritten. This isn't the best content strategy in the world, but that's what you're being asked to do, so the BEST way to handle it is to completely rewrite every post so they are 100% unique.
If you were to remove the blog posts from the other websites and simply post them on the new website, you're running the risk of taking traffic away from the already established websites.
"Would google pick up on the fact that these blogs are already appearing elsewhere on the web and thereby penalise the new site for posting material that is already indexed by Google?" -- Yes, you run the risk of being penalized by Panda with such a large amount of duplicate content. Google wants to rank websites that provide value to visitors. If a website is entirely made up of content that already exists on another website, you're providing no added value to visitors. Again, you could remove the content from the other websites and 301 redirect to the new one.... but you're taking a lot of value away from those websites if you do that.
That's a hilarious idea, btw.
Let me know if i am misunderstanding.