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I know it seems tidier to have the links to the correct domain and I would only target the higher ranking sites but don't want to embark on it if it's going to be a lot of work for only a small beneficial increase in ranking or none at all.
Identify the most important links to be updated, and contact the webmasters one by one when you get a spare moment. In your update request be sure you identify the exact page where the link is located. Provide code snippets, suggested wording, anything that would make the task easier at their end. The easier you make things the better the chance that they'll do what you ask.
Ask once, but don't chase anyone over this. They'll either do it or they won't. Don't worry about followup other than to say a quick thank you.