The problem with the SharePoint Wiki system is that it resolves the Wiki style links [[link]] at save time to absolute links to the page in the Wiki page list.
I think you will need to write some code that loops through and updates the text in your Wiki pages. Use the WSS object model to to find and update each list item that represents a Wiki page.
You can also have a look at www.sharepointproducts.com where you can download a free version of a tool (CopyMove for SharePoint) that can also move Wiki pages across site collections. It does, however, not update the links on the Wiki pages. But it is my tool - so I will give it some thought whether to add support for this. It is not the first time I have heard about this problem.