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Install SEO Manager on new site.
Set up custom redirects 301s like above. Add one at the time or import a file with urls...
Pick the target page...
Also check out documentation at
If you have any more questions, contact either mogul support or me and I'll try to help out. Redirecting an old site to new is the main use case for SEO manager so should fit your need there. I did this today for another site btw.
If you delete a page on a site that has seo manager installed it will show up in the 410 tab. This let's you easily create redirects for pages that editors have deleted.