of course backup and format is always the best way, but in cases where you have lots of stuff to reinstall, or missing programs and applications that can't find again to reinstall as well as many other reasons that you don't want to go through a clean install, you can follow my guide above.
In cases like these, for over 50 clients of mine this method has worked. If you hesitate, first backup, don't format though. Try installing the hard disk on the new MOBO after you have backed up your files, and see if my method works. If not, it's always good you have a backup huh?
to tell you the truth, I'm 100% sure this will work, not only 99%. I just don't want you to blame me in the worst case it doesn't, hence the 1%.
And besides, even if it doesn't work, your data isn't lost. You can always do a second install on the same disk without deleting the first, and move your files/documents to the new installation afterwards and delete the old installation files.