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I'm not sure how you're blocking Google from crawling external links in the robots.txt file--typically you only block them from crawling internal pages on your site. If you're using a script, though, to track the clicks on external links and that script is running your site (and you're blocking that script in robot.txt), then that still should be fine. You may want to add a "nofollow" tag on those links, though, so you don't end up passing link "credit" or "link juice" to those affiliates (unless you want to do that?). As far as external links go, though, it's typically okay (and expected) that you link out to other sites.

Along with applying the 301's and using the change of address form, I'd add submit a sitemap of the OLD urls, this encourages Google to view and assign the 301s. After a few weeks, submit the new sitemap with the NEW URls and all should be well.

As always, Google thinks it knows best. What's new? lol Good luck!