The Find and Replace tool sounds like the way to go so as not to break all of the broken links.
Yeah. If you just changed drive letters, or anything for which you can easily "find & replace all" on a particular bit of text, this would be your best bet. Restore the Library Backup, everything will be broken, but that's okay. Select all, and Rename, Move, and Copy Files in
Update Database Only mode.
In that mode, you're just fixing the links inside MC's database. The files aren't touched at all. It is just writing a new [Filename] tag to the database entry for each of the files, in fact.
Now, as it says in the article, that tool is powerful and can cause all sorts of havoc (particularly in rename mode) if you aren't paying attention. So:
1. Check through the preview panel before you click OK.
2. Try it with just a handful of files first and make sure you got everything right before you do the whole lot.
3. And, make sure, for this task, you've actually chosen Update database only mode, and not one of the
other modes in RMCF (technically, as long as the files you selected
are broken links it won't do anything to the files on disk, but the Update database only mode makes
sure).
But exactly what you need to do is exactly what that Update Database Only mode is
for in the tool. If you mess it up, just restore the Library Backup from the old machine again and try once more.